Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities

DOI10.1007/s00440-020-00991-wzbMath1470.60181arXiv1801.00761OpenAlexW3047959215MaRDI QIDQ2210745

Alexander Teplyaev, Maria Gordina, Michael Roeckner

Publication date: 8 November 2020

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.00761

zbMATH Keywords

singular perturbationOrnstein-Uhlenbeck processGirsanov theoremnon-Lipschitz monotone coefficientsnonlinear infinite-dimensional stochastic differential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Markov semigroups and applications to diffusion processes (47D07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15) Applications of operator theory in probability theory and statistics (47N30)

Related Items (2)

Existence and uniqueness for the mild solution of the stochastic heat equation with non-Lipschitz drift on an unbounded spatial domain ⋮ Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity

Cites Work

• Uniqueness for solutions of Fokker-Planck equations related to singular SPDE driven by Lévy and cylindrical Wiener noise
• Stochastic partial differential equations: an introduction
• Kolmogorov equations for stochastic PDEs.
• Heat kernel analysis on infinite-dimensional Heisenberg groups
• Functional analysis, Sobolev spaces and partial differential equations
• Heat kernel analysis on semi-infinite Lie groups
• Semigroups of linear operators and applications to partial differential equations
• Semimartingales: A course on stochastic processes
• Non-explosion, boundedness, and ergodicity for stochastic semilinear equations
• Gaussian measures in Banach spaces
• On invariant measures for diffusions on Banach spaces
• Classical Dirichlet forms on topological vector spaces --- closability and a Cameron-Martin formula
• Singular dissipative stochastic equations in Hilbert spaces
• Regularity of invariant measures for a class of perturbed Ornstein-Uhlenbeck operators
• Integrated Harnack inequalities on Lie groups
• Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups
• An application of a functional inequality to quasi-invariance in infinite dimensions
• Integration by parts and quasi-invariance for the horizontal Wiener measure on foliated compact manifolds
• Dimension-independent Harnack inequalities for subordinated semigroups
• Nonlinear semigroups in Hilbert space
• Nonlinear semigroups and evolution equations
• Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups
• The theory of generalized Dirichlet forms and its applications in analysis and stochastics
• Regularity of solutions of linear stochastic equations in hilbert spaces
• One-Parameter Semigroups for Linear Evolution Equations
• Uniqueness for stochastic evolution equations in Banach spaces
• General extinction results for stochastic partial differential equations and applications
• A few comments on a result of A. Novikov and Girsanov's theorem
• Stochastic Equations in Infinite Dimensions
• Nonlinear accretive operators in Banach spaces
• Convex Analysis
• On the Maximality of Sums of Nonlinear Monotone Operators
• Nonlinear Differential Equations of Monotone Types in Banach Spaces
• Second order PDE's in finite and infinite dimension
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