On the existence and uniqueness of solutions to stochastic differential equations of mixed Brownian and Poissonian sheet type.

DOI10.1016/S0304-4149(01)00088-6zbMath1053.60068MaRDI QIDQ1888783

Jicheng Liu

Publication date: 26 November 2004

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

zbMATH Keywords

Brownian sheetPoisson random measuretwo-parameter stochastic differential equations

Mathematics Subject Classification ID

Random fields (60G60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (7)

Stochastic differential equations driven by spatial parameters semimartingale with non-Lipschitz local characteristic ⋮ Incremental nonlinear stability analysis of stochastic systems perturbed by Lévy noise ⋮ On a type of stochastic differential equations driven by countably many Brownian motions ⋮ Global existence of solutions for stochastic impulsive differential equations ⋮ EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR STOCHASTIC IMPULSIVE DIFFERENTIAL EQUATIONS ⋮ Stochastic Differential Equation Driven by Countably Many Brownian Motions with Non-Lipschitzian Coefficients ⋮ NON-LIPSCHITZ STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTI-PARAMETER BROWNIAN MOTIONS

Cites Work

• Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane
• Existence of strong solutions for stochastic differential equations in the plane
• Uniqueness of strong solutions to stochastic differential equations in the plane with deterministic boundary process
• Stochastic integrals in the plane
• Weak martingales and stochastic integrals in the plane
• Existence and pathwise uniqueness of solutions for stochastic differential equations with respect to martingales in the plane
• The path uniqueness of the solution of the two-parameter Poisson type stochastic differential equation
• Existence of Weak Solutions to Stochastic Differential Equations in the Plane with Continuous Coefficients
• Strong solutions of stochastic differential equations for multiparameter processes
• Équations du filtrage pour un processus de poisson mélangé á deux indices
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