Particle representations for stochastic partial differential equations with boundary conditions

DOI10.1214/18-EJP186zbMath1430.60054arXiv1607.08909MaRDI QIDQ1663890

Thomas G. Kurtz, Christopher Janjigian, Dan Crisan

Publication date: 24 August 2018

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.08909

zbMATH Keywords

stochastic partial differential equationsinteracting particle systemsstochastic Allen-Cahn equationdiffusions with reflecting boundaryEuclidean quantum field theory equation with quartic interaction

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12) (L^p)-limit theorems (60F25)

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Cites Work

• Conditional distributions, exchangeable particle systems, and stochastic partial differential equations
• Weak and strong solutions of general stochastic models
• A martingale approach to the law of large numbers for weakly interacting stochastic processes
• Macroscopic limits for stochastic partial differential equations of McKean-Vlasov type
• Time reversal of diffusion processes with a boundary condition
• McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets
• Particle representations for a class of nonlinear SPDEs
• SDEs with oblique reflection on nonsmooth domains
• Characterization of stationary distributions of reflected diffusions
• A stochastic evolution equation arising from the fluctuations of a class of interacting particle systems
• Diffusion processes with boundary conditions
• Brownian Motion
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