Stochastic representation of diffusions corresponding to divergence form operators

DOI10.1016/0304-4149(96)00059-2zbMath0870.60073OpenAlexW1968303221MaRDI QIDQ1363463

Andrzej Rozkosz

Publication date: 7 August 1997

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(96)00059-2

zbMATH Keywords

diffusion processDirichlet processItô formula

Mathematics Subject Classification ID

Diffusion processes (60J60) Stochastic integrals (60H05)

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Generalization of Itô's formula for smooth nondegenerate martingales., On time-dependent functionals of diffusions corresponding to divergence form operators, A change of variable formula with applications to multi-dimensional optimal stopping problems, Unnamed Item, On the Feynman–Kac representation for solutions of the Cauchy problem for parabolic equations in divergence form, Dirichlet processes associated to diffusions, BSDE driven by Dirichlet process and semi-linear parabolic PDE. Application to homogeniza\-tion., Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem, A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients, Existence and regularity of infinitesimally invariant measures, transition functions and time-homogeneous Itô-SDEs, Stochastic differential equations driven by processes generated by divergence form operators II: convergence results, An extension of Itô's formula for elliptic diffusion processes, A probabilistic interpretation of the divergence and BSDE's., A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE.

Cites Work

• Stochastic calculus related to non-symmetric Dirichlet forms
• On existence and stability of weak solutions of multidimensional stochastic differential equations with measurable coefficients
• Time reversal of diffusions
• Some properties of Markov processes associated with time dependent Dirichlet forms
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Decomposition of Dirichlet processes and its applications
• On a martingale method for symmetric diffusion processes and its applications
• Diffusion processes with non-smooth diffusion coefficients and their density functions
• On conditional diffusion processes
• On a construction of Markov processes associated with time dependent Dirichlet spaces
• Weak convergence of diffusions corresponding to divergence form operators
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