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In probability theory, an excursion probability is the probability that a stochastic process surpasses a given value in a fixed time period. It is the
Excursion_probability
Uncontrolled nuclear fission chain reaction
chain reaction. It is sometimes referred to as a critical excursion, critical power excursion, divergent chain reaction, or simply critical. Any such event
Criticality_accident
Diving mode and decompression technique
the effect of pressure variation due to excursions away from holding pressure, thereby reducing the probability and amount of bubble formation due to these
Saturation_diving
Stochastic process
In probability theory a Brownian excursion process (BPE) is a stochastic process that is closely related to a Wiener process (or Brownian motion). Realisations
Brownian_excursion
Formula in probability theory
autocorrelation of x(t) at 0. Rice's formula can be used to approximate an excursion probability P { sup t ∈ [ 0 , 1 ] X ( t ) ≥ u } {\displaystyle \mathbb {P} \left\{\sup
Rice's_formula
Two closely related models for generating random graphs
David (1997-04-01). "Brownian excursions, critical random graphs and the multiplicative coalescent". The Annals of Probability. 25 (2). doi:10.1214/aop/1024404421
Erdős–Rényi_model
Emeritus Professor of Statistics and Mathematics
(1992-03-01). "Size-biased sampling of Poisson point processes and excursions". Probability Theory and Related Fields. 92 (1): 21–39. doi:10.1007/BF01205234
Jim_Pitman
Book by Claude Dellacherie and Paul-André Meyer
Probabilities and Potential (titled Probabilités et Potentiel in the original French) is a mathematics book written by Claude Dellacherie and Paul-André
Probabilities_and_Potential
(1992). "Size-biased sampling of Poisson point processes and excursions". Probability Theory and Related Fields. 92: 21–39. doi:10.1007/BF01205234. Perman
Pitman–Yor_process
Hypothesis test in mathematics
The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald and later proven to be optimal by Wald
Sequential probability ratio test
Sequential_probability_ratio_test
Probability theory term
is formalized in probability theory by conditioning. Conditional probabilities, conditional expectations, and conditional probability distributions are
Conditioning_(probability)
Concept in probability theory
Tree (CRT) is a random real tree that can be defined from a Brownian excursion. The Brownian tree was defined and studied by David Aldous in three articles
Brownian_tree
relational model Probability Probability bounds analysis Probability box Probability density function Probability distribution Probability distribution function
List_of_statistics_articles
French mathematician (1886-1971)
December 1971) was a French mathematician who was active especially in probability theory, introducing fundamental concepts such as local time, stable distributions
Paul_Lévy_(mathematician)
Stochastic process generalizing Brownian motion
(1979). "A relation between Brownian bridge and Brownian excursion". Annals of Probability. 7 (1): 143–149. doi:10.1214/aop/1176995155. JSTOR 2242845
Wiener_process
Reversal of direction of Earth's magnetic field
only a few hundred years (such as the Laschamp excursion). These events are classified as excursions rather than full geomagnetic reversals. Stable polarity
Geomagnetic_reversal
1889 train wreck in Armagh, Ireland
finding: This terrible calamity would in all human probability have been prevented had the excursion train been fitted with an automatic continuous brake
Armagh_rail_disaster
many mathematical contexts, in particular geometric group theory and probability theory. They are also the simplest examples of Gromov hyperbolic spaces
Real_tree
Swiss-American engineer and educator
taking colleagues and family out for excursions on the San Francisco Bay. On his many field trips and academic excursions, he took thousands of pictures, many
Hans_Albert_Einstein
Sustained nuclear fission achieved solely by prompt neutron emission
assembly is critical if every released neutron has a 1/2.4 = 0.42 = 42 % probability of causing another fission event as opposed to either being absorbed
Prompt_criticality
Concept in statistics
a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is also called
Gaussian_random_field
French mathematician, statistician
Nathalie Eisenbaum is a French mathematician, statistician, and probability theorist. She works as a director of research with the Centre national de
Nathalie_Eisenbaum
Stochastic process in physics
a continuous-time gaussian process B(t) whose probability distribution is the conditional probability distribution of a standard Wiener process W(t)
Brownian_bridge
Japanese mathematician (born 1935)
to probability theory, stochastic processes and stochastic differential equations. He is revered as a luminary in the field of modern probability theory
Shinzo_Watanabe
French mathematician
Andreas E. (2021). "A Lifetime of Excursions Through Random Walks and Lévy Processes" (PDF). Progress in Probability. 78: 4. Retrieved 29 March 2025. Barlow
Jean_Bertoin
Number, approximately 3.14
result that the probability of two random numbers being relatively prime (that is, having no shared factors) is equal to 6/π2. This probability is based on
Pi
American mathematician (born 1981)
centers on arithmetic statistics, with excursions into related questions in arithmetic geometry and probability theory.[citation needed] Wood was born
Melanie_Wood
1972 book on parapsychology
ISSN 0007-1773. Gridgeman, N. T. (1975-01-01). "THE ROOTS OF COINCIDENCE: AN EXCURSION INTO PARAPSYCHOLOGY, Arthur Koestler". World Futures. 14 (3): 307–312
The_Roots_of_Coincidence
Laurel Smith; Persi Diaconis (1988). "Honest bernoulli excursions". Journal of Applied Probability. 25 (3): 464–477. doi:10.2307/3213976. JSTOR 3213976
Brownian motion and Riemann zeta function
Brownian_motion_and_Riemann_zeta_function
Analytic function in mathematics
Pitman, Jim; Yor, Marc (2001). "Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions". Bulletin of the American
Riemann_zeta_function
Process by which atoms or molecules acquire charge by gaining or losing electrons
singly or multiply charged ions. The ionization rate, i.e. the ionization probability in unit time, can be calculated using quantum mechanics. (There are classical
Ionization
Heritage railway in Cumbria, England
connections that were established in 1869. During the summer season, excursion trains from Lancashire and elsewhere used the east-to-north side of Plumpton
Lakeside and Haverthwaite Railway
Lakeside_and_Haverthwaite_Railway
Mukhopadhyay and others have suggested that the Laschamps geomagnetic excursion, a short reversal of Earth's magnetic field around 41,000 years ago, may
Neanderthal_extinction
British mathematician
Andreas E., eds. (2021). "A Lifetime of Excursions Through Random Walks and Lévy Processes". Progress in Probability. 78: 1–4. Retrieved 1 August 2025. Ron
Ron_Doney
Probability distribution
The Tracy–Widom distribution is a probability distribution from random matrix theory introduced by Craig Tracy and Harold Widom (1993, 1994). It is the
Tracy–Widom_distribution
Welsh mathematician
David Williams FRS is a Welsh mathematician who works in probability theory. David Williams was born at Gorseinon, near Swansea, Wales. He was educated
David Williams (mathematician)
David_Williams_(mathematician)
Severe events involving radioactive materials
A criticality accident (also sometimes referred to as an "excursion" or "power excursion") occurs when a nuclear chain reaction is accidentally allowed
Nuclear and radiation accidents and incidents
Nuclear_and_radiation_accidents_and_incidents
In probability theory and statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for
Continuous-time stochastic process
Continuous-time_stochastic_process
Representation of a type of random process
A, Vol. 131, 518–532. Theodoridis, Sergios (2015-04-10). "Chapter 1. Probability and Stochastic Processes". Machine Learning: A Bayesian and Optimization
Autoregressive_model
Number divisible only by 1 and itself
proven at the end of the 19th century, which says roughly that the probability of a randomly chosen large number being prime is inversely proportional
Prime_number
Stratovolcano in Kagoshima Prefecture, Japan
eruption would have about a 5% probability of temporarily closing the six largest airports in Japan and above a 80% probability of closing the major Kyushu
Sakurajima
Collision between a vehicle and a bird
water and shelter increase bird strike probability. The characteristics of an aircraft also affect the probability of a bird strike occurring. Turbofan
Bird_strike
Solution to a stochastic differential equation
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion
Diffusion_process
1968 book by Robert M. Blumenthal and Ronald K. Getoor
compactification, Lévy systems, characteristic measures, the Martin boundary, and excursion theory. At 11:40 Getoor says "in the summer of [19]60 Blumenthal and I
Markov Processes and Potential Theory
Markov_Processes_and_Potential_Theory
Branch of mathematics
Artists". Calculus training materials at imomath.com Archived 9 July 2023 at the Wayback Machine (in English and Arabic) The Excursion of Calculus, 1772
Calculus
Alive" January 15, 1961 (1961-01-15) 11 "Physics and Games – Laws of Probability" January 22, 1961 (1961-01-22) 12 "The Face of the Moon" January 29, 1961 (1961-01-29)
List of The Nature of Things episodes
List_of_The_Nature_of_Things_episodes
Change in the heritable traits of populations
161281098. PMC 55389. PMID 11470913. Felsenstein, Joseph (November 1979). "Excursions along the Interface between Disruptive and Stabilizing Selection". Genetics
Evolution
Bed of material at a runway's end to stop aircraft overrun
of runway excursions worldwide may turn out to be much more cost-effective than the current focus on reducing the already very low probability of occurrence
Engineered materials arrestor system
Engineered_materials_arrestor_system
Film series
2030. Chitti is now a museum exhibit. A curious school student on an excursion trip asks her guide why it was dismantled, to which Chitti responds, "Naan
Enthiran_(film_series)
Method for describing dice rolls
to discuss probability distribution in an article, "Dice as Random Number Generators", in the inaugural issue of fanzine Alarums & Excursions (1975). The
Dice_notation
Volcanic eruption in New Zealand
the island at the time. Of these people, 38 were passengers on a shore excursion from the cruise ship Ovation of the Seas, which was on a 12-day voyage
2019 Whakaari / White Island eruption
2019_Whakaari_/_White_Island_eruption
dedicated to Liberty 1815 The Excursion: Preface to the Edition 1814 1795–1814 "'On Man, on Nature, and on Human Life," The Excursion 1814 Book First: The Wanderer
List of poems by William Wordsworth
List_of_poems_by_William_Wordsworth
Reduction in pressure to lower than normal sea level atmospheric pressure
excursions from sea level to altitudes above 15,000 feet (4,600 m) without oxygen prebreathing may induce venous gas bubbles, with a 5% probability of
Hypobaric_decompression
2018 video game
life. The development team had previously carried out a similar research excursion to Nepal during development of Far Cry 4. As the development team was
Far_Cry_5
Disorder caused by dissolved gases forming bubbles in tissues
harmlessly eliminated through respiration, or by decompression by an upward excursion from a condition of saturation by the inert breathing gas components,
Decompression_sickness
Stochastic volatility model used in derivatives markets
payoff max ( F T − K , 0 ) {\displaystyle \max(F_{T}-K,\;0)} under the probability distribution of the process F t {\displaystyle F_{t}} . Except for the
SABR_volatility_model
1991 aircraft accident in Thailand
Klausen, Val Gardena, Olang, Mals and Kiens, who had participated in an excursion to the Far East under the guidance of Clemens August Andreae. The other
Lauda_Air_Flight_004
Aborted Moon landing mission in the Apollo program
was designed to shut the engine down in response to chamber pressure excursions. Pogo oscillations had occurred on Titan rockets (used during the Gemini
Apollo_13
Son of Pope Alexander VI (c. 1476 – 1497)
Rome. It was a sign of this friendship that they rode together during an excursion of the papal court through the city to Saint John Lateran on 5 May 1493
Giovanni Borgia, 2nd Duke of Gandía
Giovanni_Borgia,_2nd_Duke_of_Gandía
Large minefield laid by the United States in World War I
temporarily marking the end point of a mining excursion to avoid leaving an unmined gap when the next excursion started. These buoys were subject to potential
North_Sea_Mine_Barrage
Facility for supporting saturation diving projects
is stand-by diver to the working divers. Each diver is supplied by an excursion umbilical from inside the bell. The bell has a set of high pressure gas
Saturation_diving_system
Process in mathematical probability theory
(1977). "Weak convergence to Brownian meander and Brownian excursion". The Annals of Probability. 5 (1): 117–129. doi:10.1214/aop/1176995895. Revuz, Daniel;
Brownian_meander
President and Dictator of Mexico from 1876 to 1911
February 1864. Díaz's hold was consolidated enough that he began making excursions into Veracruz, and Minatitlán was taken by 28 March 1864. Meanwhile, French
Porfirio_Díaz
English polymath (1642–1727)
Mathematica. pp. 142–146. Hykšová, Magdalena. GEOMETRIC PROBABILITY APPLICATIONS THROUGH HISTORICAL EXCURSION (PDF). ESU-6. Hykšová, Magdalena; Kalousová, Anna;
Isaac_Newton
Third period of the Paleozoic Era
throughout the Silurian, evidenced by numerous major carbon and oxygen isotope excursions during this geologic period. Sea levels rose from their Hirnantian low
Silurian
U.S. government cryptographic standard
module's normal operating ranges for voltage and temperature. Intentional excursions beyond the normal operating ranges may be used by an attacker to thwart
FIPS_140-2
District of London, England
place for growing vegetables to feed London. The manor became a popular excursion destination for Londoners, attracted to the area by its rural feel. Many
Islington
Event that is both extremely large in effect and of unique origins
gray ones", in the sense that the power law model gives non-negligible probability to large events. In a variety of studies it has been found that, despite
Dragon_king_theory
Stochastic processes in mathematics
of Doob's martingale convergence theorems. By bounding the probability of extreme excursions of the sample paths, it ensures that martingales with bounded
Doob's_martingale_inequality
Oldest-surviving crustal material from the Hadean eon
zircons detected around the world are over four billion years old. The probability of discovering so much as a single zircon over four billion years in
Hadean_zircon
Red dwarf star in the constellation Aquarius
simulations exist, such as the "Exoplanet Travel Bureau" and the "Exoplanets Excursion"—both by NASA. Scientific accuracy has been a point of discussion both
TRAPPIST-1
Climate interval
carbon excursion is called the Monterey Carbon Excursion, which is globally recorded but mainly in the Circum-Pacific Belt. The Monterey Excursion seems
Middle Miocene Climatic Optimum
Middle_Miocene_Climatic_Optimum
Large baleen whale species
area updated. Fin whales are regularly encountered on whale-watching excursions worldwide. In Monterey Bay and the Southern California Bight, fin whales
Fin_whale
Nuclear reactor where water boils in core
formation, making the neutron moderation less efficient and the fission probability lower. In normal operation, the control rods are only used to keep a
Boiling_water_reactor
Pitman, Jim; Yor, Marc (2001). "Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions". Bull. Amer. Math. Soc. (N
Lévy's_stochastic_area
Carvalho N, Bablani L, Wilson N, Stevenson M (28 September 2020). "The probability of the 6-week lockdown in Victoria (commencing 9 July 2020) achieving
COVID-19_lockdowns
Branch of elementary mathematics
Courier Corporation. ISBN 978-0-486-31981-0. Kleiner, Israel (2012). Excursions in the History of Mathematics. Springer Science & Business Media. ISBN 978-0-8176-8268-2
Arithmetic
Climatic cooling after the Medieval Warm Period (16th–19th centuries)
the various proxy reconstructions relate to the magnitude of past cool excursions, principally during the twelfth to fourteenth, seventeenth and nineteenth
Little_Ice_Age
Time taken by a signal to change to a high value
either positive or negative step response, even if a displayed negative excursion is popularly termed fall time. Rise time is an analog parameter of fundamental
Rise_time
Systematic study of people and cultures
of the Western Pacific (1922) by Bronisław Malinowski, Ethnologische Excursion in Johore (1875) by Nicholas Miklouho-Maclay, Coming of Age in Samoa (1928)
Ethnography
Early photographic technique
Duperly, a Frenchman, produced a booklet of Daguerreotypes, Daguerian Excursions in Jamaica, being a collection of views ... taken on the spot with the
Daguerreotype
Directed graph where each vertex pair has one arc
Lajos (1991), "A Bernoulli Excursion and Its Various Applications", Advances in Applied Probability, 23 (3), Applied Probability Trust: 557–585, doi:10.2307/1427622
Tournament_(graph_theory)
Orbits where planets may have liquid surface water
Williams, D.; Pollard, D. (2002). "Earth-like worlds on eccentric orbits: excursions beyond the habitable zone". International Journal of Astrobiology. 1 (1):
Habitable_zone
Rapid transit system serving the San Francisco Bay Area
entering and exiting at the same station within 30 minutes incurred an "excursion fare" of $6.40 – significantly higher than many station-to-station fares
Bay_Area_Rapid_Transit
Preserved American 2-8-2 locomotive
first time in twenty-six years, and on July 11, No. 14 pulled its first excursion train from Duluth to Two Harbors with a Christening ceremony. The highlight
Duluth and Northern Minnesota 14
Duluth_and_Northern_Minnesota_14
National park in New Mexico, United States
footprints along the dunes as evidence of the nightly hunting and foraging excursions of nocturnal animals. Carnivorans include coyotes, bobcats, badgers, and
White_Sands_National_Park
Music genre that uses electronic instruments
music, which is a composing method that uses mathematical probability systems. Different probability algorithms were used to create a piece under a set of
Electronic_music
1919 book by John Maynard Keynes
leading economist. As an academic, Keynes had worked on his Treatise on Probability, which includes a critique of conventional economic thinking under conditions
The Economic Consequences of the Peace
The_Economic_Consequences_of_the_Peace
Algorithm for computing greatest common divisors
integers. The probability of a given quotient q is approximately ln |u/(u − 1)| where u = (q + 1)2. For illustration, the probability of a quotient of
Euclidean_algorithm
Zante, Athens, Smyrna, and Constantinople, providing passengers with excursions and guided tours. Dental fillings: First mentioned by Cornelius Celsus
List of Italian inventions and discoveries
List_of_Italian_inventions_and_discoveries
"Absolute dating of the European Neolithic using the 5259 BC rapid 14C excursion", Nature Communications, 2024 doi:10.1038/s41467-024-48402-1 Höflmayer
Chronology of the ancient Near East
Chronology_of_the_ancient_Near_East
Equipment allowing or assisting the user to breathe in a hostile environment
user interface of the control and monitoring system can influence the probability of operator error. The endurance of a rebreather or life support system
Breathing_apparatus
Laser science process
atom absorbing n photons then emitting a single high energy photon. The probability of absorbing n photons decreases as n increases, explaining the rapid
High_harmonic_generation
Strong surface-level winds that radiate from a single point
Airport (ALA)". aviation-safety.net. Retrieved 12 September 2022. "Runway excursion, USAir Inc., Flight 183, McDonnell Douglas DC9-31, N964VJ, Detroit Metropolitan
Downburst
Cube that fits through hole in smaller cube
University Press, pp. 54–55. Reprinted as Ogilvy, C. Stanley (1994), Excursions in mathematics, New York: Dover Publications Inc., ISBN 0-486-28283-X
Prince_Rupert's_cube
Tabulated data to facilitate safe diving ascents
tables. 1% Risk tables are tables which satisfy the condition of a high probability (c0.95) of a low risk (c0.01) of producing symptomatic decompression
Decompression_tables
American mathematician (1929–2017)
the University of California, San Diego. Getoor's research deals with probability theory, especially the theory of Markov processes and potential theory
Ronald_Getoor
Natural history museum in Manhattan, New York
". Irving Press. Preston, Douglas (1986). Dinosaurs in the Attic: An Excursion into the American Museum of Natural History. New York City: St. Martin's
American Museum of Natural History
American_Museum_of_Natural_History
Statistical experiment designs
calculation of these probabilities, usually as a function of F ( x ) {\displaystyle F(x)} . Assuming that transition probabilities are fixed in time, depending
Up-and-down_design
lectures. Robert J. Adler, "On excursion sets, tube formulas and maxima of random fields", The Annals of Applied Probability 2000, Vol. 10, No. 1, 1–74.
Large deviations of Gaussian random functions
Large_deviations_of_Gaussian_random_functions
EXCURSION PROBABILITY
EXCURSION PROBABILITY
Girl/Female
Arabic, Hindu, Indian, Kannada, Marathi, Muslim, Sindhi
Pleasure Trip; Excursion Spot
Biblical
exclusion; separation
Surname or Lastname
English
English : in all probability an English variant of Scottish Lachlan (see McLachlan), altered through folk etymology. However, Black cites one John sine terra (c. 1180–1214), suggesting that the surname could have arisen quite literally as a nickname for a man with no land.
Surname or Lastname
English
English : habitational name from Middle English, Old French ju(ie)rie ‘Jewish quarter’, often denoting a non-Jew living in the Jewish quarter of a town, rather than a Jew. Most medieval English cities had their Jewish quarters, at least until King Edward I’s attempted expulsion of the Jews from England in 1290. This did not succeed in expelling the Jews, but it did give a license to persecution and so broke up many of the old Jewish quarters.
Girl/Female
Muslim
Pleasure trip, Excursion spot
Girl/Female
Biblical
House of expulsion.
Male
English
Anglicized form of Hebrew Gereshom, GERSHOM means "exile, expulsion." In the bible, this is the name of several characters, including a son of Moses.
Girl/Female
Muslim/Islamic
Excursion spot
Girl/Female
Biblical
Exclusion, separation.
Male
Hebrew
(גֵּרְש×ׄ×) Hebrew name GERESHOM means "exile, expulsion." In the bible, this is the name of several characters, including a son of Moses.
Male
English
Anglicized form of Hebrew Gereshown, GERSHON means "exile, expulsion." In the bible, this is the name of the first son of Levi.Â
Girl/Female
Biblical
House of expulsion.
Male
Hebrew
(גֵּרְש×ï‹×Ÿ) Hebrew name GERESHOWN means "exile, expulsion." In the bible, this is the name of the first son of Levi.Â
Girl/Female
Arabic, Muslim
Pleasure Trip; Excursion Spot
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : in all probability from the Swale river in Yorkshire. (Reaney and Wilson list a 17th-century example, Swayles, with this origin.) Alternatively, it may be a metronymic from the Old Norse female personal name Svala.
EXCURSION PROBABILITY
EXCURSION PROBABILITY
Girl/Female
Hindu, Indian, Kannada
Small; Beautiful
Boy/Male
Hindu, Indian
God who is Fond of Devotees
Girl/Female
Bengali, Hindu, Indian, Marathi, Telugu
To Cross over to the Other World
Boy/Male
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim
The Moon
Boy/Male
Arabic, Muslim
Supporter of Islam
Girl/Female
Hindu
Self connected
Boy/Male
Native American
two rivers running.
Surname or Lastname
English
English : variant spelling of Keel.Perhaps an Americanized spelling of German Kehl or Kühl (see Kuhl).
Boy/Male
Afghan, Arabic, Celebrity, Hindu, Indian, Kannada, Muslim, Sindhi, Tamil, Traditional
Full; Prosperous; Amply Settled; Civilised
Girl/Female
Indian
King
EXCURSION PROBABILITY
EXCURSION PROBABILITY
EXCURSION PROBABILITY
EXCURSION PROBABILITY
EXCURSION PROBABILITY
n.
The act of thrusting or pushing out; a driving out; expulsion.
n.
An excursion.
n.
A brief or rapid journey; an excursion or jaunt.
n.
The act of rowing; excursion in a rowboat.
a.
Prone to make excursions; wandering; roving; exploring; as, an excursive fancy.
n.
An excursion for plundering.
n.
A riding out; an excursion.
n.
A wandering about; excursion; a roving.
v.
Extent or space taken in by anything excursive; compass or extent of excursion; reach; scope; discursive power; as, the range of one's voice, or authority.
n.
A flowing; also, a hostile incursion.
n.
A large omnibus used for excursions.
n.
The act of excusing; seizure by law.
n.
An excursion.
v.
An excursion from the usual track; range; digression; deviation.
n.
A pleasure excursion; a trip.
n.
Same as Occursion.