Variational calculation of Laplace transforms via entropy on Wiener space and applications

DOI10.1016/j.jfa.2014.07.006zbMath1306.60064arXiv1402.6576OpenAlexW2963849077MaRDI QIDQ457613

Ali Süleyman Üstünel

Publication date: 29 September 2014

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

Full work available at URL: https://arxiv.org/abs/1402.6576

zbMATH Keywords

entropystochastic differential equationvariational calculusMalliavin calculusinvertibilityWiener space

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items

Gibbs Measure for the Focusing Fractional NLS on the Torus ⋮ Phase transitions for \(\phi^4_3\) ⋮ Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions ⋮ On the variational method for Euclidean quantum fields in infinite volume ⋮ Invariant Gibbs dynamics for the two-dimensional Zakharov-Yukawa system ⋮ A variational method for \(\Phi^4_3\) ⋮ Martingale representation for degenerate diffusions ⋮ Causal transport plans and their Monge–Kantorovich problems ⋮ On global solutions of the random Hamilton–Jacobi equations and the KPZ problem ⋮ KPZ reloaded ⋮ The KPZ equation on the real line ⋮ Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations ⋮ The Boué-Dupuis formula and the exponential hypercontractivity in the Gaussian space ⋮ Optimal transport maps on infinite dimensional spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The construction of filtrations on abstract Wiener space
• The realization of positive random variables via absolutely continuous transformations of measure on Wiener space
• Entropy, invertibility and variational calculus of adapted shifts on Wiener space
• A variational representation for certain functionals of Brownian motion
• The notion of convexity and concavity on Wiener space
• An introduction to analysis on Wiener space
• Solution of the Monge-Ampère equation on Wiener space for general log-concave measures
• Persistence of invertibility on the Wiener space
• An Example of a Stochastic Differential Equation Having No Strong Solution
• Representation of the distributions on Wiener space and stochastic calculus of variations