The heat equation and reflected Brownian motion in time-dependent domains.

DOI10.1214/aop/1079021464zbMath1046.60060OpenAlexW2075243787MaRDI QIDQ1879869

Krzysztof Burdzy, Zhen-Qing Chen, John Sylvester

Publication date: 15 September 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1079021464

zbMATH Keywords

stochastic differential equationlocal timereflecting Brownian motiontime-dependent domain

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Heat equation (35K05) Applications of stochastic analysis (to PDEs, etc.) (60H30)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Reflection Brownian motions: Quasimartingales and strong Caccioppoli sets
• Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
• Efficient Markovian couplings: Examples and counterexamples
• On reflecting Brownian motion - a weak convergence approach
• A conditioned limit theorem for random walk and Brownian local time on square root boundaries
• Excursions in a cone for two-dimensional Brownian motion
• Stochastic differential equations for multi-dimensional domain with reflecting boundary
• Stochastic differential equations with reflecting boundary condition in convex regions
• The Skorohod oblique reflection problem in domains with corners and application to stochastic differential equations
• On reflecting diffusion processes and Skorokhod decompositions
• A construction of reflecting barrier Brownian motions for bounded domains
• Brownian motion in a Brownian crack
• Large time asymptotics for Brownian hitting densities of transient concave curves
• Weak convergence of reflecting Brownian motions
• The heat equation and reflected Brownian motion in time-dependent domains. II: Singularities of solutions.
• On a construction of diffusion processes on moving domains
• Reflection and coalescence between independent one-dimensional Brownian paths
• Uniqueness for reflecting Brownian motion in Lip domains
• Stochastic bifurcation models
• The heat equation and reflected Brownian motion in time-dependent domains.
• A Skorokhod-type lemma and a decomposition of reflected Brownian motion
• A critical case for Brownian slow points
• Reflecting Brownian motions and a deletion result for Sobolev spaces of order \((1,2)\)
• SDEs with oblique reflection on nonsmooth domains
• Multi-dimensional diffusion and the Markov process on the boundary
• \(L^ 2\) solvability and representation by caloric layer potentials in time-varying domains
• Construction and decomposition of reflecting diffusions on Lipschitz domains with Hölder cusps
• On the Poisson Kernel for the Neumann Problem of Schrödinger Operators
• A comparison theorem for conditioned Markov processes
• Fundamental solutions of parabolic differential equations and boundary value problems
• The Semimartingale Structure of Reflecting Brownian Motion
• Stochastic differential equations with reflecting boundary conditions
• A new approach to the skorohod problem, and its applications
• A new approach to the Skorohod problem, and its applications
• The first-passage density of the Brownian motion process to a curved boundary
• Diffusions and Elliptic Operators
• The method of layer potentials for the heat equation in time-varying domains
• A harnack inequality for parabolic differential equations
• Diffusion processes with boundary conditions
• On the path of an inert object impinged on one side by a Brownian particle

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