L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel

DOI10.1016/0022-1236(82)90036-2zbMath0488.60068OpenAlexW2039297296MaRDI QIDQ1166196

Philip Trauber, Bernard Gaveau

Publication date: 1982

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(82)90036-2

zbMATH Keywords

Ornstein-Uhlenbeck processesstochastic variations calculus of P. Malliavin

Mathematics Subject Classification ID

Generalized stochastic processes (60G20) Stochastic integrals (60H05)

Related Items (36)

Quantum and non-causal stochastic calculus ⋮ Generalized stochastic integrals and the Malliavin calculus ⋮ Quantitative normal approximations for the stochastic fractional heat equation ⋮ Quantum stochastic calculus with maximal operator domains. ⋮ Stochastic variation of constants formula for infinite dimensional equations ⋮ SMOOTH PROBABILITY MEASURES AND ASSOCIATED DIFFERENTIAL OPERATORS ⋮ Stochastic calculus with anticipating integrands ⋮ The Itô formula for anticipative processes with nonmonotonous time scale via the Malliavin calculus ⋮ Occupation densities of stratonovitch stochastic differential equations with boundary conditions ⋮ Central limit theorems for stochastic wave equations in dimensions one and two ⋮ Time reversal for infinite-dimensional diffusions ⋮ Gaussian measures on linear spaces ⋮ The doob‐meyer decomposition for anticipating processes ⋮ Stochastic anticipative calculus on the path space over a compact Riemannian manifold ⋮ Gaussian fluctuations for the stochastic heat equation with colored noise ⋮ Generalized multiple stochastic integrals and the representation of wiener functionals ⋮ Extension of the ito calculus via the malliavin calculus ⋮ Itô's lemma without non-anticipatory conditions ⋮ Finite dimensional approximation of Riemannian path space geometry. ⋮ Anticipating stochastic Volterra equations ⋮ A central limit theorem for the stochastic heat equation ⋮ Averaging 2D stochastic wave equation ⋮ Transformation of Wiener measure under anticipative flows ⋮ Representation of the distributions on Wiener space and stochastic calculus of variations ⋮ Interacting Brownian particles and Gibbs fields on pathspaces ⋮ Equations différentielles sur l'espace de Wiener et formules de Cameron- Martin non-linéaires ⋮ Stochastic calculus with respect to Gaussian processes ⋮ A central limit theorem for the stochastic wave equation with fractional noise ⋮ Stochastic calculus with respect to Gaussian processes ⋮ Integral representation of renormalized self-intersection local times ⋮ Generalized holomorphic processes and differentiability ⋮ Spatial ergodicity for SPDEs via Poincaré-type inequalities ⋮ Differentiable measures and the Malliavin calculus ⋮ Explicit stochastic analysis of Brownian motion and point measures on Riemannian manifolds ⋮ Differential calculus on finite codimensional submanifolds of the Wiener space: The divergence operator ⋮ Malliavin calculus and Euclidean quantum mechanics. I: Functional calculus

Cites Work

• The Malliavin calculus, a functional analytic approach
• On a Generalization of a Stochastic Integral

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