Markovian integral equations

DOI10.1214/19-AIHP958zbMath1465.60064arXiv1701.03272OpenAlexW3004815699MaRDI QIDQ2179235

Yanyan Li

Publication date: 12 May 2020

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.03272

zbMATH Keywords

integral equationMarkov processmild solutionFeynman-Kac formulasuperprocesspath-dependent PDElog-Laplace equation

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Applications of stochastic analysis (to PDEs, etc.) (60H30) Systems of nonlinear integral equations (45G15) Second-order parabolic systems (35K40) Semilinear parabolic equations (35K58)

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Cites Work

• A control problem with fuel constraint and Dawson-Watanabe superprocesses
• A probabilistic approach to one class of nonlinear differential equations
• A weighted occupation time for a class of measure-valued branching processes
• Path processes and historical superprocesses
• Branching particle systems and superprocesses
• Semigroups of linear operators and applications to partial differential equations
• Construction and regularity of measure-valued Markov branching processes
• Superdiffusion and parabolic nonlinear differential equations
• Path-dependent equations and viscosity solutions in infinite dimension
• Ordinary differential equations. An introduction to nonlinear analysis. Transl. from the German by Gerhard Metzen
• On the support of solutions to stochastic differential equations with path-dependent coefficients
• On viscosity solutions of path dependent PDEs
• A limit theorem of branching processes and continuous state branching processes
• BSDE, path-dependent PDE and nonlinear Feynman-Kac formula
• Functional Kolmogorov equations
• An Introduction to Branching Measure-Valued Processes