Existence and pathwise uniqueness of solutions for stochastic differential equations with respect to martingales in the plane

DOI10.1016/S0304-4149(99)00040-XzbMath0997.60066MaRDI QIDQ1613644

Zongxia Liang

Publication date: 29 August 2002

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

zbMATH Keywords

pathwise uniquenesstwo-parameter martingalesstochastic differential equations in the plane

Mathematics Subject Classification ID

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

Related Items (10)

On the existence and uniqueness of solutions to stochastic differential equations of mixed Brownian and Poissonian sheet type. ⋮ Homeomorphic property of solutions of SDE driven by countably many Brownian motions with non-Lipschitzian coefficients ⋮ Stochastic differential equations driven by spatial parameters semimartingale with non-Lipschitz local characteristic ⋮ Stochastic inclusions and set-valued stochastic equations with mixed integrals in the plane ⋮ On a type of stochastic differential equations driven by countably many Brownian motions ⋮ ANTICIPATING MULTIDIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH REFLECTIONS ⋮ KUNITA-TYPE STOCHASTIC FLOWS OF HOMEOMORPHISMS IN EUCLIDEAN SPACE ⋮ Spatial asymptotic behavior of homeomorphic global flows for non-Lipschitz SDEs ⋮ 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

• Quasi sure quadratic variations of two parameter smooth martingales on the Wiener space
• 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
• Two-parameter martingales and their quadratic variation
• Stochastic integrals in the plane
• Weak martingales and stochastic integrals in the plane
• Differentiation formulas for stochastic integrals in the plane
• An extension of stochastic integrals in the plane
• On the uniqueness of solutions of stochastic differential equations
• Predictable and dual predictable projections of two-parameter stochastic processes
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