In stochastic analysis, a rough path is a generalization of the classical notion of a smooth path. It extends calculus and differential equation theory...

using rough paths theory, while adding a chosen definition of iterated integrals of Brownian motion, it is possible to define a deterministic rough integral...

of unbounded variation. The rough path integral, which is defined for functions equipped with some additional "rough path" structure and generalizes stochastic...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

complexity Kolmogorov complexity estimates Hidden Markov model states Rough path signature Surrogate time series and surrogate correction Loss of recurrence...

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....

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...

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...

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...

In the 1990s and 2000s the theories of Schramm–Loewner evolution and rough paths were introduced and developed to study stochastic processes and other...

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...

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...

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...

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...

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...

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...