Smoothness of Itô maps and diffusion processes on path spaces (I)

DOI10.1016/j.ansens.2006.07.001zbMath1127.60033OpenAlexW2022671909MaRDI QIDQ3421429

Terence J. Lyons, Xiang Dong Li

Publication date: 13 February 2007

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2006_4_39_4_649_0

zbMATH Keywords

rough pathsItô mapfractional like Brownian motion

Mathematics Subject Classification ID

Brownian motion (60J65) Sample path properties (60G17) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (16)

Nonautonomous Young differential equations revisited ⋮ Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory ⋮ Monotonic homotopy for trajectories of Young systems ⋮ Regularity of the Itô-Lyons map ⋮ Positivity of the density for rough differential equations ⋮ Sensitivity of rough differential equations: an approach through the omega lemma ⋮ Geometric aspects of Young integral: decomposition of flows ⋮ Laplace approximation for rough differential equation driven by fractional Brownian motion ⋮ An approximation to Wiener measure and quantization of the Hamiltonian on manifolds with non-positive sectional curvature ⋮ Rough integrators on Banach manifolds ⋮ Uniqueness for the signature of a path of bounded variation and the reduced path group ⋮ Controlled differential equations as Young integrals: a simple approach ⋮ Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion ⋮ Regular trajectories of Young systems ⋮ Yet another introduction to rough paths ⋮ A generalized change of variable formula for the Young integral

Cites Work

• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• Differential equations driven by rough signals
• Finite dimensional approximations to Wiener measure and path integral formulas on manifolds
• Differentiability of six operators on nonsmooth functions and \(p\)-variation. With the collaboration of Jinghua Qian
• A class of vector fields on path spaces
• Integration by parts and quasi-invariance for heat kernel measures on loop groups
• Stochastic Jacobi fields and vector fields induced by varying area on path spaces
• Existence and uniqueness of geodesics on path spaces
• Stochastic analysis, rough path analysis and fractional Brownian motions.
• Sobolev spaces and capacities theory on path spaces over a compact Riemannian manifold
• Lévy area of Wiener processes in Banach spaces
• Differential equations driven by rough signals. I: An extension of an inequality of L. C. Young
• System Control and Rough Paths
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