scholarly journals Rough path theory and stochastic calculus

2019 ◽  
Vol 32 (1) ◽  
pp. 113-136
Author(s):  
Yuzuru Inahama
Keyword(s):  
Stochastic Calculus ◽  
Rough Path ◽  
Rough Path Theory

scholarly journals Good rough path sequences and applications to anticipating stochastic calculus

2007 ◽  
Vol 35 (3) ◽  
pp. 1172-1193 ◽  
Author(s):  
Laure Coutin ◽  
Peter Friz ◽  
Nicolas Victoir
Keyword(s):  
Stochastic Calculus ◽  
Rough Path ◽  
Anticipating Stochastic Calculus

scholarly journals Rough Path Theory to Approximate Random Dynamical Systems

2021 ◽  
Vol 20 (2) ◽  
pp. 997-1021
Author(s):  
H. Gao ◽  
M. J. Garrido ◽  
A. Gu ◽  
K. Lu ◽  
B. Schmalfuß
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Rough Path ◽  
Rough Path Theory

New Directions in Rough Path Theory

2021 ◽  
Vol 17 (4) ◽  
pp. 1955-2019
Author(s):  
Thomas Cass ◽  
Dan Crisan ◽  
Peter Friz ◽  
Massimiliano Gubinelli
Keyword(s):  
New Directions ◽  
Rough Path ◽  
Rough Path Theory

scholarly journals Wong–Zakai Approximation for Landau–Lifshitz–Gilbert Equation Driven by Geometric Rough Paths

2021 ◽  
Author(s):  
Kistosil Fahim ◽  
Erika Hausenblas ◽  
Debopriya Mukherjee
Keyword(s):  
Maximal Regularity ◽  
Correction Term ◽  
Regularity Property ◽  
One Dimension ◽  
Rough Paths ◽  
Point Of Interest ◽  
Convergence Results ◽  
Regular Approximation ◽  
Rough Path ◽  
Rough Path Theory

AbstractWe adapt Lyon’s rough path theory to study Landau–Lifshitz–Gilbert equations (LLGEs) driven by geometric rough paths in one dimension, with non-zero exchange energy only. We convert the LLGEs to a fully nonlinear time-dependent partial differential equation without rough paths term by a suitable transformation. Our point of interest is the regular approximation of the geometric rough path. We investigate the limit equation, the form of the correction term, and its convergence rate in controlled rough path spaces. The key ingredients for constructing the solution and its corresponding convergence results are the Doss–Sussmann transformation, maximal regularity property, and the geometric rough path theory.

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