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 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 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

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.

scholarly journals ANOTHER APPROACH TO SOME ROUGH AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 535-550 ◽  
Author(s):  
JOSEF TEICHMANN
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Solution Process ◽  
Partial Differential ◽  
State Spaces ◽  
New Approach ◽  
Finite Dimensional ◽  
Rough Path ◽  
Rough Path Theory

In this paper, we introduce a new approach to rough and stochastic partial differential equations (RPDEs and SPDEs): we consider general Banach spaces as state spaces and — for the sake of simplicity — finite dimensional sources of noise, either rough or stochastic. By means of a time-dependent transformation of state space and rough path theory, we are able to construct unique solutions of the respective R- and SPDEs. As a consequence of our construction, we can apply the pool of results of rough path theory, in particular we can obtain strong and weak numerical schemes of high order converging to the solution process.

Sociocultural memory development research drives new directions in gadgetry science

2019 ◽  
Vol 42 ◽  
Author(s):  
Penny Van Bergen ◽  
John Sutton
Keyword(s):  
Episodic Memory ◽  
Autobiographical Memory ◽  
Developmental Psychology ◽  
Cross Cultural ◽  
Memory Development ◽  
Development Research ◽  
Cultural Research ◽  
New Directions ◽  
Cross Cultural Research

Abstract Sociocultural developmental psychology can drive new directions in gadgetry science. We use autobiographical memory, a compound capacity incorporating episodic memory, as a case study. Autobiographical memory emerges late in development, supported by interactions with parents. Intervention research highlights the causal influence of these interactions, whereas cross-cultural research demonstrates culturally determined diversity. Different patterns of inheritance are discussed.

Sign in / Sign up

Export Citation Format

Share Document