NON-LIPSCHITZ STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTI-PARAMETER BROWNIAN MOTIONS-Reference-Cited by-同舟云学术

NON-LIPSCHITZ STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTI-PARAMETER BROWNIAN MOTIONS

Published:2006-09 Issue:03 Volume:06 Page:329-340
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

ZHANG XICHENG¹,ZHU JINGYANG¹

Affiliation:

1. Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China

Abstract

By proving an extension of nonlinear Bihari's inequality (including Gronwall's inequality) to multi-parameter and non-Lebesgue measure, in this paper we first prove by successive approximation the existence and uniqueness of solution of stochastic differential equation with non-Lipschitz coefficients and driven by multi-parameter Brownian motion. Then we study two discretizing schemes for this type of equation, and obtain their L2-convergence speeds.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021949370600175X

Reference20 articles.

1. Modulus of continuity of the canonic Brownian motion “on the group of diffeomorphisms of the circle”

2. Une inegalite pour martingales a indices multiples et ses applications

3. Stochastic integrals in the plane

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