Lévy area of Wiener processes in Banach spaces

DOI10.1214/aop/1023481002zbMath1016.60071OpenAlexW1995738788MaRDI QIDQ1872270

Zhongmin Qian, Terence J. Lyons, Michel Ledoux

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1023481002

zbMATH Keywords

Brownian motionLévy arearough paths

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (26)

Laplace's method for the laws of heat processes on loop spaces ⋮ Young integrals and SPDEs ⋮ Asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths ⋮ Random dynamical systems, rough paths and rough flows ⋮ Solving mean field rough differential equations ⋮ Optimal extension to Sobolev rough paths ⋮ A general framework for waves in random media with long-range correlations ⋮ Random attractors for rough stochastic partial differential equations ⋮ Non-linear rough heat equations ⋮ A stochastic Taylor-like expansion in the rough path theory ⋮ Limit theorem for a differential equation with a long-range random coefficient ⋮ From constructive field theory to fractional stochastic calculus. II: Constructive proof of convergence for the Lévy area of fractional Brownian motion with Hurst index \(\alpha \in \left(\frac{1}{8},\frac{1}{4}\right)\) ⋮ An extension theorem to rough paths ⋮ Rough paths analysis of general Banach space-valued Wiener processes ⋮ Weak Poincaré inequalities on domains defined by Brownian rough paths ⋮ Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem ⋮ A rough path over multidimensional fractional Brownian motion with arbitrary Hurst index by Fourier normal ordering ⋮ A generalized Fernique theorem and applications ⋮ Two-parameter \(p,q\)-variation paths and integrations of local times ⋮ Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations ⋮ Stochastic calculus for fractional Brownian motion with Hurst exponent \(H>\frac 1 4 \): A rough path method by analytic extension ⋮ Yet another introduction to rough paths ⋮ Rough flows ⋮ Smoothness of Itô maps and diffusion processes on path spaces (I) ⋮ Large deviations and support theorem for diffusion processes via rough paths. ⋮ On the signature of a path in an operator algebra

Cites Work

• Rates of clustering for some Gaussian self-similar processes
• Gaussian measures in Banach spaces
• Flow of diffeomorphisms induced by a geometric multiplicative functional
• Differential equations driven by rough signals
• Stochastic area for Brownian motion on the Sierpiński gasket
• Approximation, metric entropy and small ball estimates for Gaussian measures
• Extending the Wong-Zakai theorem to reversible Markov processes
• Stochastic analysis, rough path analysis and fractional Brownian motions.
• Some small ball probabilities for Gaussian processes under nonuniform norms
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• On stochastic convolution in banach spaces and applications
• System Control and Rough Paths
• The Lévy area process for the free Brownian motion
• Stochastic Equations in Infinite Dimensions
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