Reflecting diffusions on Lipschitz domains with cusps -- analytic construction and Skorohod representation

DOI10.1007/BF01053454zbMath0840.60070OpenAlexW4249270166MaRDI QIDQ1902485

Masatoshi Fukushima, Matsuyo Tomisaki

Publication date: 1 February 1996

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01053454

zbMATH Keywords

Dirichlet formelliptic operatorreflecting diffusion process

Mathematics Subject Classification ID

Probabilistic potential theory (60J45) Local time and additive functionals (60J55)

Related Items (11)

Skorokhod decomposition for a reflected -strong Feller diffusion with singular drift ⋮ On the third boundary value problem in domains with cusps ⋮ On approximation of the Dirichlet problem for divergence form operators by Robin problems ⋮ Regularity and well-posedness of some quasi-linear elliptic and parabolic problems with nonlinear general Wentzell boundary conditions on nonsmooth domains ⋮ Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains ⋮ Construction and strong Feller property of distorted elliptic diffusion with reflecting boundary ⋮ Regularity of solutions of linear second order elliptic and parabolic boundary value problems on Lipschitz domains ⋮ On a strict decomposition of additive functionals for symmetric diffusion processes ⋮ Uniqueness of Schrödinger operators restricted in a domain ⋮ Doubly Feller property of Brownian motions with Robin boundary condition ⋮ On a decomposition of symmetric diffusions with reflecting boundary conditions.

Cites Work

• Unnamed Item
• Reflection Brownian motions: Quasimartingales and strong Caccioppoli sets
• Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
• Upper bounds for symmetric Markov transition functions
• Superposition of diffusion processes
• A construction of reflecting barrier Brownian motions for bounded domains
• On an \(L^p\)-estimate of resolvents of Markov processes
• On the semimartingale representation of reflecting Brownian motion in a cusp
• Dirichlet forms and symmetric Markov processes
• On a strict decomposition of additive functionals for symmetric diffusion processes
• General boundary conditions for multi-dimensional diffusion processes
• Reflecting Brownian Motion in a Cusp
• The Semimartingale Structure of Reflecting Brownian Motion
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• A construction of diffusion processes with singular product measures

This page was built for publication: Reflecting diffusions on Lipschitz domains with cusps -- analytic construction and Skorohod representation