From random walks to rough paths

DOI10.1090/S0002-9939-09-09930-4zbMath1179.60017arXiv0810.2681OpenAlexW2085243688MaRDI QIDQ3182587

Emmanuel Breuillard, Peter K. Friz, Martin Huesmann

Publication date: 9 October 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.2681

zbMATH Keywords

Donsker's theoremrough paths, random walks on nilpotent Lie groups

Mathematics Subject Classification ID

Functional limit theorems; invariance principles (60F17) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (14)

Smooth approximation of stochastic differential equations ⋮ Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs ⋮ Ballistic random walks in random environment as rough paths: convergence and area anomaly ⋮ Weak approximation of a fractional SDE ⋮ Cubature on Wiener space: pathwise convergence ⋮ Random walks and Lévy processes as rough paths ⋮ Homogenisation for anisotropic kinetic random motions ⋮ A (rough) pathwise approach to a class of non-linear stochastic partial differential equations ⋮ Central limit theorems for non-symmetric random walks on nilpotent covering graphs. I ⋮ Area anomaly in the rough path Brownian scaling limit of hidden Markov walks ⋮ Rough path stability of (semi-)linear SPDEs ⋮ Canonical RDEs and general semimartingales as rough paths ⋮ Rough invariance principle for delayed regenerative processes ⋮ Rough path recursions and diffusion approximations

Cites Work

• Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula
• Differential equations driven by rough paths. Ecole d'Eté de Probabilités de Saint-Flour XXXIV -- 2004. Lectures given at the 34th probability summer school, July 6--24, 2004.
• On uniform exponential growth for solvable groups.
• Donsker's invariance principle for Lie groups
• Differential equations driven by rough signals
• Multidimensional Stochastic Processes as Rough Paths
• PROBABILITIES ON LIE GROUPS
• System Control and Rough Paths
• On Convergence of Stochastic Processes
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