A generalized Fernique theorem and applications

DOI10.1090/S0002-9939-2010-10528-2zbMath1202.60057arXiv1004.1923OpenAlexW1979318272MaRDI QIDQ3053513

Peter K. Friz, Harald Oberhauser

Publication date: 29 October 2010

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

Full work available at URL: https://arxiv.org/abs/1004.1923

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic analysis (60H99) Probability theory on algebraic and topological structures (60B99)

Related Items (22)

A moment estimate of the derivative process in rough path theory ⋮ The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory ⋮ Precise Laplace asymptotics for singular stochastic PDEs: the case of 2D gPAM ⋮ Fractal dimensions of rough differential equations driven by fractional Brownian motions ⋮ Constrained rough paths ⋮ Integrability and tail estimates for Gaussian rough differential equations ⋮ Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes ⋮ Quasi sure large deviation for increments of fractional Brownian motion in Hölder norm ⋮ Super-Gaussian decay of exponentials: a sufficient condition ⋮ Rough paths and SPDE ⋮ Laplace approximation for rough differential equation driven by fractional Brownian motion ⋮ Malliavin calculus and rough paths ⋮ A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations ⋮ Smoothness of the density for solutions to Gaussian rough differential equations ⋮ Density of the signature process of fBm ⋮ Small ball probabilities, metric entropy and Gaussian rough paths ⋮ Integrability on the abstract Wiener space of double sequences and Fernique theorem ⋮ Precise asymptotics: robust stochastic volatility models ⋮ Integrability of (Non-)Linear Rough Differential Equations and Integrals ⋮ Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations ⋮ The two-dimensional KPZ equation in the entire subcritical regime ⋮ ASYMPTOTIC EXPANSION OF THE DENSITY FOR HYPOELLIPTIC ROUGH DIFFERENTIAL EQUATION

Cites Work

• 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.
• Differential equations driven by Gaussian signals
• Lévy area of Wiener processes in Banach spaces
• Laplace's method for the laws of heat processes on loop spaces
• Approximations of the Brownian rough path with applications to stochastic analysis
• A note on the notion of geometric rough paths
• Exact asymptotic estimates of Brownian path variation
• Non-degeneracy of Wiener functionals arising from rough differential equations
• System Control and Rough Paths
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