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Concept in stochastic analysis
In stochastic analysis, a rough path is a generalization of the classical notion of a smooth path. It extends calculus and differential equation theory
Rough_path
Differential equations involving stochastic processes
using rough paths theory, while adding a chosen definition of iterated integrals of Brownian motion, it is possible to define a deterministic rough integral
Stochastic differential equation
Stochastic_differential_equation
Operation in mathematical calculus
of unbounded variation. The rough path integral, which is defined for functions equipped with some additional "rough path" structure and generalizes stochastic
Integral
Transportation route connecting one location to another
turning and through traffic onto a one-way circular roadway Trail/track, a rough path through more wild or remote territory Many other types of road Strait
Thoroughfare
Non-linear stochastic partial differential equation
awarded the Fields Medal for this work on the KPZ equation, along with rough paths theory and regularity structures. There were 6 different analytic self-similar
Kardar–Parisi–Zhang_equation
Green sand beach in Kaʻū district, Hawai'i, US
surrounded by pasturelands and is only legally accessible by foot. The paths are rugged due to both illegal vehicular traffic and erosion. The land owner
Papakōlea_Beach
Austrian mathematician
awarded an ERC Consolidator Grant. with Hairer, Martin (2020). A Course on Rough Paths. Universitext (2nd ed.). Springer Cham. doi:10.1007/978-3-030-41556-3
Peter_Friz
Headland in County Wicklow, Ireland
person. The footpath, after the initial section with cut steps, is a rough path formed by rainwater and ascending through natural woodland. A more gradual
Bray_Head
Monolith in Mauritania
road that runs from Atar to Zouerrat. Drivers can be hired in Atar. The rough path runs parallel to the tracks for the Iron Ore Train before crossing it
Ben_Amera
Greenock, Inverclyde, Scotland
Cross of Lorraine combined with an anchor. Across the road, steps and a rough path lead up to a viewpoint at Craigs Top with views up the River Clyde as
Lyle_Hill
2000 Bollywood drama film
and this breaks his heart. He decides to shed his innocence, takes the rough path to propose her, and ends up being a don in town. Manoj Bajpayee as Ram
Dil_Pe_Mat_Le_Yaar!!
Lebanese based writer, activist, attorney, and professor (born 1972)
fundamentalist past and to finally pursue his ultimate goal of personal freedom. A rough path that leaves him a traitor to Hezbollah, a suspected terrorist to the United
Rami_Ollaik
Mountain on the Isle of Man
railway station (last railway stop before the summit) from which there is a rough path to the peak. The trail has sections of gravel, slate stones, grass and
Snaefell
Y = f ( Y ) d X {\displaystyle dY=f(Y)\,dX} driven by the path X. The theory of rough paths generalises the Young integral and Young differential equations
P-variation
Historic migration route spanning Independence, MO–Oregon City, OR
where they split from the main trail and followed (and improved) the rough path known as Hastings Cutoff, used by the ill-fated Donner Party in 1846.
Oregon_Trail
US Army cavalry regiment (1898)
The Rough Riders was a nickname given to the 1st United States Volunteer Cavalry, one of three such regiments raised in 1898 for the Spanish–American
Rough_Riders
British mathematician
finance. In particular he developed what is now known as the theory of rough paths. Together with Patrick Kidger he proved a universal approximation theorem
Terry_Lyons_(mathematician)
Hiking trail in Bhutan
ends in Trongsa and from there to Bumthang District, taking through the rough paths of the Himalayas and up to as high as 5000m above sea level. The route
Snowman_Trek
Computer graphics method
Path tracing is a rendering algorithm in computer graphics that simulates how light interacts with objects and participating media to generate realistic
Path_tracing
Mountain of the southern Scottish Highlands
ridge to the Bealach an Dubh Choirein. From this bealach a series of rough paths cut very steeply up the right side of the prominent buttress, involving
Stùc_a'_Chroin
Hill in Snowdonia, Wales
from Nantmor Mountain Centre at Gelli-Iago. From this an intermittent rough path runs from West of Clogwyn Coch up to the two small lakes. The hill can
Yr_Arddu_(South)
Collection of random variables
In the 1990s and 2000s the theories of Schramm–Loewner evolution and rough paths were introduced and developed to study stochastic processes and other
Stochastic_process
Hill (486m) in Monmouthshire, Wales
reached. The main path follows the crest of the mountain north to the trig point and chapel remains which mark the summit. A rough path follows the perimeter
Skirrid_Fawr
Valley in Highland, Scotland
of waterfalls. The top of the path leads out onto the shoulder formed by the ancient landslip, with views and a rough path to the flat corrie floor. This
Coire_Gabhail
Tamil Hindu saint and poet
equivalent to performing abhisekam and puja. Once, while walking on a rough path, a thorn pricked and pierced Pamban Swami’s foot, causing him intense
Pamban_Swamigal
Mathematician
projections. In a similar vein, and with rough differential equations in mind, the study of non-geometric rough paths on manifolds has been approached in Armstrong
Damiano_Brigo
Narrow strip of land in Afghanistan
There is a rough road from Ishkashim to Sarhad, Afghanistan built in the 1960s and improved in the 2020s, but only rough paths beyond. These paths run some
Wakhan_Corridor
Online action role-playing game
Path of Exile is a 2013 free-to-play action role-playing video game developed and published by Grinding Gear Games. Following an open beta phase, the game
Path_of_Exile
Chapel in Knaresborough, North Yorkshire, England
dedicated to St Mary, is a Grade I Listed Building that is reached via a narrow path and steps from Abbey Road. The Chapel has a carved altar with a canopied
Chapel of Our Lady of the Crag
Chapel_of_Our_Lady_of_the_Crag
Objects that generalize functions
(simplified) algebra is maybe the most popular in use today. Inspired by Lyons' rough path theory, Martin Hairer proposed a consistent way of multiplying distributions
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Sequence of data points over time
complexity Kolmogorov complexity estimates Hidden Markov model states Rough path signature Surrogate time series and surrogate correction Loss of recurrence
Time_series
American football player and coach (born 1992)
Tommy Rees stats. Sports.espn.go.com. Retrieved on August 9, 2012. "A Rough Path: The Tale of Tommy Rees". Down the Tunnel. November 18, 2013. Watson,
Tommy Rees (American football)
Tommy_Rees_(American_football)
German schlager musician and songwriter
Wolfgang Petry 1983 Wahnsinn Madness Wolfgang Petry 1984 Rauhe Wege Rough Paths Wolfgang Petry 1987 Mit offenen Armen With Open Arms Wolfgang Petry 1988
Wolfgang_Petry
Mountain in Scotland
livestock from raiders or hide cattle they themselves had stolen. The steep rough path up from Glen Coe skirts a wooded ravine and is a popular short walk (around
Bidean_nam_Bian
stopped at Kurumalai station from where the villagers used to take a rough path to reach their homes. Of late, buses do ply into the village and pass
Kalugasalapuram
South Korean musician (born 2001)
Korean shoegaze musician. He has released four solo albums: Let's Walk on the Path of a Blue Cat (2020), To See the Next Part of the Dream (2021), After the
Parannoul
National news agency of Taiwan
ISBN 9789004227699. Wu, Wan-yu (May 1, 1994). "改革路上多崎嶇 — 唐盼盼與中央社" [The rough path of reform: Tang Pan-pan and the Central News Agency]. Commonwealth Magazine
Central_News_Agency_(Taiwan)
City in Massachusetts, United States
(5 km) stretch with Massachusetts Route 2. Route 2, which follows the rough path of (and is nicknamed after) the Mohawk Trail, enters over the Fall River
Greenfield,_Massachusetts
Unincorporated community in Washington, United States
his growing customer base, James Longmire's son, Elcaine, constructed a rough path from the resort to Paradise Park around 1885. In 1892 (or possibly 1895)
Paradise,_Washington
Reconstructed historic site in Fort Lee, New Jersey, United States
Washington, Cornwallis marched his men up the cliffs of the Palisades via a rough path, and southward through the Northern Valley. The landing was long erroneously
Fort_Lee_Historic_Park
British mathematician (1905–2000)
also is named after him and has now been generalised in the theory of rough paths. Laurence Chisholm Young was born in Göttingen, the fifth of the six
Laurence_Chisholm_Young
Technique used for determining crystal structures and identifying mineral compounds
Since it is difficult to visualize all the atoms at once, the ribbon shows the rough path of the protein's backbone from its N-terminus to its C-terminus.
X-ray_crystallography
Granite monolith in Queensland, Australia
different routes to the top, by road or by goat track. The Goat Track is a rough path that consists of 758 individual stairs from start to finish. Castle Hill
Castle_Hill,_Townsville
Suburban trail in Melbourne, Australia
The EastLink Trail is a shared use path for cyclists and pedestrians in the outer eastern/southeastern suburbs of Melbourne, Victoria, Australia. The trail
EastLink_Trail
Expedition from south to north poles using only surface transport
Scott Polar Research Institute. Rough map of the expedition (based on the official route graphic). Red shows the rough path; cyan shows the 0- and 180-degree
Transglobe_Expedition
Mountain in Lombardy, Italy
From Bondone to the lock of this pass are five miles of arduous and rough path for laden horses... The other is Count Gerolamo di Conces also of the
Monte_Cingolo_Rosso
American journalist
behind. Bryant's group took the Hastings Cutoff, a shorter but much rougher path that took them through the Great Salt Lake Desert. Bryant was concerned
Edwin_Bryant_(alcalde)
Austrian-British mathematician
analysis techniques, theory of homogenisation, theory of path sampling and theory of rough paths and, in 2014, on his theory of regularity structures. Under
Martin_Hairer
Alternate name for Vale of Neath, Wales
Carboniferous Coal Measures. The falls are difficult of access with only a rough path reaching them from the vicinity of Sgwd Gwladus downstream and requiring
Waterfall_Country_(Wales)
Footpath in Northern Catalonia
ISBN 9780679032168. Retrieved 28 October 2012. Guides, Rough; Lloyd, Chris (2002-09-01). The Rough Guide to Costa Brava. Rough Guides. pp. 153–. ISBN 9781858288024. Retrieved
Camí_de_Ronda
Census-designated place in South Carolina, United States
near the plantation houses) for horse and wagons. These dirt paths were crude rough paths that bore no resemblance to today's modern highways. Highway
Murrells Inlet, South Carolina
Murrells_Inlet,_South_Carolina
Scottish mathematician
S2CID 118678520. Davie, A. M. (2007). "Differential equations driven by rough paths: An approach via discrete approximation". arXiv:0710.0772 [math.PR].
Alexander_Munro_Davie
Fingeroth Oct. 1993 Trial by Jury Part 2. Spider-Man pleads guilty. 385 Rough Justice Michelinie/Bagley Danny Fingeroth Nov. 1993 Trial by Jury Part 3
List of The Amazing Spider-Man issues
List_of_The_Amazing_Spider-Man_issues
followed what is now M-123 and M-28 while the southern route followed the rough path of today's US 2. The highway was designated as a memorial following Theodore
Theodore Roosevelt International Highway
Theodore_Roosevelt_International_Highway
Nucleus of the rostral midbrain involved in motor coordination
human midbrain at the level of the superior colliculus, that shows the rough path of each nervus oculomotorius from its nucleus toward the eye and the relative
Magnocellular_red_nucleus
Journalist A K Astbury (1987) also examines the word roddin, which means a rough path or a track trodden by sheep. He says that in north Lincolnshire, a roading
Roddon
Poem by Du Mu
(Chinese: 杜牧; pinyin: Dù Mù). Going to a distant mountain to climbing the stone path, people reside in the depth of white clouds. I had to stop my carriage to
Shan_Xing
without being seen") Fallschirmaufklärer: Per aspera ad astra (Latin for "Rough paths lead to the stars") Panzergrenadiere: in corde veritas (Latin for "truth
List of military unit mottoes by country
List_of_military_unit_mottoes_by_country
American baseball player (born 1988)
Nation. Retrieved May 2, 2015. Davis, Craig (August 29, 2013). "Dyson took rough path to Marlins". Sun-Sentinel. Archived from the original on December 23,
Sam_Dyson
State highway in Colorado, United States
the Ute people. The future eastern half of Highway 82 came first, as a rough path over Independence Pass that soon reached Aspen. A private company improved
Colorado_State_Highway_82
wheel Talbot 700 Tripoli Tripoli Grand Prix Practice Car bounced on the rough surface of the road, went into the right embankment, hit a small wall, rolled
List of driver deaths in motorsport
List_of_driver_deaths_in_motorsport
an alliance between Britain and France and ending their historic rivalry Rough Riders 1997 1898 Depicts The Battle of San Juan Hill, part of the Spanish–American
List of historical films set in Near Eastern and Western civilization
List_of_historical_films_set_in_Near_Eastern_and_Western_civilization
Tor on Bodmin Moor, Cornwall, England
Rough Tor (/ˈraʊtər/), or Roughtor, is a tor on Bodmin Moor, Cornwall, England, United Kingdom. The site comprises the tor summit and logan stone, a Neolithic
Rough_Tor
Dynamical study of growth of a surface
Popular tools include statistical mechanics, renormalization group, rough path theory, etc. Kinetic Monte Carlo (KMC) is a form of computer simulation
Surface_growth
Interstate 84 travels east–west, following the Columbia River and the rough path of the old Oregon Trail from Portland east to Idaho. For this reason,
Transportation_in_Oregon
Research institute in Bangalore, India
differential equations Probability theory Ergodic Theory and dynamical systems Rough path theory, stochastic analysis Random Geometry, point processes Complex analysis
TIFR Centre for Applicable Mathematics
TIFR_Centre_for_Applicable_Mathematics
Hiking trail in Highland, Scotland
North Highland Way varies hugely, crossing beaches, forests, road and rough paths as well as some remote areas.[citation needed] The Herald reported in
North_Highland_Way
Cave in province of Chieti, Italy
stalagmites, flowstone, and rimstone pools. It has electric lighting with rough paths, concrete steps, and iron bridges. Gabriele D'Annunzio employed the cave
Grotta_del_Cavallone
1955 film by Satyajit Ray
Pather Panchali (Bengali pronunciation: [pɔtʰer pãtʃali] , transl. Song Of The Little Road) is a 1955 Indian drama film written and directed by Satyajit
Pather_Panchali
Extinct breed of horse
frugality. Paul Diffloth praised its ability to trot at 12 km/h (7.5 mph) on rough paths. Maturing late, it was suitable for work after age seven. Compact like
Bidet_horse
1990 studio album by Sandra Mihanovich and Celeste Carballo
although perhaps not directly. I still believe that it left us a less rough path for those of us who came much later. It is a very brave album today. To
Mujer_contra_mujer_(album)
Long-distance footpath in England
The South West Coast Path is England's second-longest waymarked long-distance footpath, after the King Charles III England Coast Path, and is designated
South_West_Coast_Path
United States Navy commander (1886–1941)
two months that Koehler spent on Sims' staff were far removed from the rough seas and fumes of the subchasers. "I have landed among the very smart and
Hugo_W._Koehler
2010. Bloom did kill two other women (drug addicts who did not survive rough sex), gives the location of their bodies, and kills himself. Another Honduran
List_of_Elementary_episodes
"beginning of the end" or "just a dream or nightmare".[citation needed] Rough Night In a mid-credits scene, Pippa sings lyrics that allude to the evening
List of films with post-credits scenes
List_of_films_with_post-credits_scenes
Indian religion and philosophy
century. According to tradition, the Buddha instructed his followers in a path of cultivation that leads to awakening and full liberation from dukkha (lit
Buddhism
Icelandic magical stave intended as a wayfinder
Icelandic magical stave intended to help the bearer find their way through rough weather. The symbol is attested in the Huld Manuscript (1860), and does
Vegvísir
Civil parish in Derbyshire, England
as Grassmore in Chesterfield parish registers from 1568. Only a few rough paths crossed the "moor" at this time, from north to south diagonally one ran
Grassmoor, Hasland and Winsick
Grassmoor,_Hasland_and_Winsick
Mountain in Colorado, United States
a trail for about 2 miles (3.2 km) to treeline. From there, there's a rough path on talus (scree) up the southwest ridge of the peak for an additional
West_Spanish_Peak
Interstate Highway in Michigan, United States
the Michigan Legislature; at the time, Division 6 corresponded to the rough path of today's I-94. In 1919, the Michigan State Highway Department (MSHD)
Interstate_94_in_Michigan
Fictional character in the NBC medical drama
from the pilot episode until the eleventh-season finale. Carter's career path is one of the main story arcs of the series, beginning as a third-year medical
John_Carter_(ER)
series: Wild Things (1998) Wild Things 2 (2004) Wild Things: Diamonds in the Rough (2005) Wild Things: Foursome (2010) The Wild Thornberrys Movie (2002) Wild
List_of_films:_U–W
Brand of recreational diving rebreathers
mounted inside a stainless steel protective housing/frame suitable for rough handling and use as a bailout rebreather. The unit's buoyancy fluctuates
KISS_Rebreathers
American Southwest to designate difficult-going countryside strewn with rough lava flows or rocks, and now used to designate the rock found in such country
Meanings of minor-planet names: 6001–7000
Meanings_of_minor-planet_names:_6001–7000
Road in Hong Kong
Wan King Path (Chinese: 灣景街; lit. 'Bayview Path') is a road in Sai Kung Town, New Territories, Hong Kong. It is located next to the main public square
Wan_King_Path
American singer-songwriter (born 1941)
announced a series of tours which were billed as the "Rough and Rowdy Ways World Wide Tour". The Rough and Rowdy Ways World Tour replaced Dylan's varied set
Bob_Dylan
Open space in Sheffield, England
Bole Hill Road consists mostly of woodland and scrub crisscrossed by rough paths. Bole Hill Wood covers an area of 4.22 hectares and is made of mixed
Bolehill_Recreation_Ground
Signal attenuation in telecommunications
Path loss, or path attenuation, is the reduction in power density (attenuation) of an electromagnetic wave as it propagates through space. Path loss is
Path_loss
2005 video game
Fire Emblem: Path of Radiance is a 2005 tactical role-playing game developed by Intelligent Systems and Nintendo SPD, and published by Nintendo for the
Fire_Emblem:_Path_of_Radiance
American singer (1958–2009)
attended his concerts, which spread messages of love and healing during rough economic and political times. His presence in the Middle East was considered
Michael_Jackson
Group of islands in the South Atlantic
recorded as sighted in 1506 by Portuguese explorer Tristão da Cunha, though rough seas prevented a landing. He believed them to be uninhabited and named the
Tristan_da_Cunha
Swedish electronic music duo
acts to be on the big stage. Hedberg called the group's early years as "rough" partly due to his fear of flying which he did not conquer until 2009, which
Carbon_Based_Lifeforms
Computer graphics technique
applications using shaders or offline applications using ray tracing or path tracing. Starting in the 1980s, a number of rendering researchers worked
Physically_based_rendering
Australian 2/16th Infantry Battalion's flanks and threatened to isolate it. A rough path, circling to the east and back to Dump 1, was found. Dump 1 is the first
First Battle of Eora Creek–Templeton's Crossing
First_Battle_of_Eora_Creek–Templeton's_Crossing
various other dirt logging roads, as evidenced on earlier maps, make out a rough path of the current roadway. In November 1995, the first part of Carolina Forest
Carolina_Forest_Boulevard
1594 Portuguese military campaign against the Kingdom of Kandy
exhausted by days of fighting, were forced to fight for each step along rough paths through thick forests. One by one they fell. Captain Álvaro de Souza
Campaign_of_Danture
Businessman and public official (born 1971)
to journalists in 2018. It used Tesla Model Xs and was reported to be a rough ride while traveling at suboptimal speeds. Two tunnel projects announced
Elon_Musk
Degree of difficulty of a walking trail
walk, mainly on poorly maintained path or tracks, through rough fields or woods. There may be steep climbs, rough uneven terrain or frequent stiles."
Trail difficulty rating system
Trail_difficulty_rating_system
2007 Singaporean TV series or program
The Golden Path (Chinese: 黄金路) is a 30-episode drama serial. Set in 1982 and spanning 25 years, it tells the story of a family embroiled in conflicts of
The_Golden_Path_(TV_series)
Algorithm used for pathfinding and graph traversal
weighted graph, a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from source to goal. One major practical
A*_search_algorithm
ROUGH PATH
ROUGH PATH
Boy/Male
Gaelic
Rough.
Surname or Lastname
English
English : habitational name from a place so named in Humberside. Recorded in Domesday Book as Rutha, the place name may derive from Old Norse hrúedhr ‘rough shaly ground’.
Surname or Lastname
Scottish
Scottish : variant of Tulloch. In Scotland it is pronounced tyookh.English : nickname for a valiant or stubborn person, from Middle English togh, tow(e) ‘steadfast’.
Boy/Male
Hindu
Rough, Rugged
Boy/Male
Gaelic, Hindu, Indian, Irish
Rough; Small Rough One
Boy/Male
Australian, British, Christian, English, French, Irish
Spear-friend; Rough; Little Rough One
Boy/Male
Gaelic
Rough.
Boy/Male
Gaelic
Rough.
Boy/Male
Gaelic Irish
Rough.
Boy/Male
Gaelic
Rough.
Boy/Male
Gaelic
Rough.
Boy/Male
Irish
Rough.
Surname or Lastname
English (Cornwall)
English (Cornwall) : unexplained.
Boy/Male
Irish
Rough; rugged.
Surname or Lastname
English and Irish (pronounced Bow)
English and Irish (pronounced Bow) : variant spelling of Bow.English (pronounced Boff) : from a Norman form of Old French boeuf ‘bull’, ‘ox’, hence a nickname for a powerfully built man, or in some cases a metonymic occupational name for a herdsman.
Boy/Male
Irish
Rough peace.
Boy/Male
Tamil
Rough, Rugged
Surname or Lastname
English
English : habitational name from any of various places, for example in Cheshire and Derbyshire, so named from Old English hÅh ‘spur of a hill’ (literally ‘heel’). This widespread surname is especially common in Lancashire.Irish (County Limerick) : variant of Haugh 1.
Surname or Lastname
English
English : habitational name from any of various places called Brough, of which there are several in Yorkshire and Derbyshire as well as elsewhere. The place name is from Old English burh ‘fortress’ and in most cases these are the sites of Roman fortifications. The pronunciation is usually ‘bruff’.Possibly an altered spelling of German Brauch.
Boy/Male
Gaelic Irish
Rough.
ROUGH PATH
ROUGH PATH
Girl/Female
Gujarati, Hindu, Indian, Modern
Pleasant
Girl/Female
Latin
Triumphant.
Girl/Female
Latin American
Of Mars. Feminine of Marcus. Mars was mythological Roman god of fertility also identified with...
Boy/Male
Indian
Girl/Female
American, Australian, British, English, Greek
A Flowering Vine; The Name of a Flowering Vine Used in Folk Medicine
Boy/Male
Muslim
Servant of the one, Servant of God
Boy/Male
Indian
Always to Win
Girl/Female
Indian
Starting place of the river Ganga
Boy/Male
Indian, Tamil
Important; Prime
Girl/Female
Indian
Care, Concern
ROUGH PATH
ROUGH PATH
ROUGH PATH
ROUGH PATH
ROUGH PATH
n.
Tempestuous; boisterous; stormy; as, rough weather; a rough day.
superl.
Stiff; rigid; not flexible; stubborn; as, a tough bow.
n.
Not courteous or kind; harsh; rude; uncivil; as, a rough temper.
n.
Marked by coarseness; shaggy; ragged; disordered; -- said of dress, appearance, or the like; as, a rough coat.
superl.
Severe; violent; as, a tough storm.
v. t.
To tint with rouge; as, to rouge the face or the cheeks.
v. i.
To paint the face or cheeks with rouge.
v. t.
To cut or make in a hasty, rough manner; -- with out; as, to rough out a carving, a sketch.
n.
Having inequalities, small ridges, or points, on the surface; not smooth or plain; as, a rough board; a rough stone; rough cloth.
v. t.
To render rough; to roughen.
n.
Marked by severity or violence; harsh; hard; as, rough measures or actions.
adv.
In a rough manner; rudely; roughly.
n.
Austere; harsh to the taste; as, rough wine.
a.
Feather-footed; as, a rough-footed dove.
n.
Not polished; uncut; -- said of a gem; as, a rough diamond.
superl.
Not easily separated; viscous; clammy; tenacious; as, tough phlegm.
n.
Hastily or carelessly done; wanting finish; incomplete; as, a rough estimate; a rough draught.
a.
Like dough; soft.
n.
Loud and hoarse; offensive to the ear; harsh; grating; -- said of sound, voice, and the like; as, a rough tone; rough numbers.