Strong approximations of stochastic differential equations with jumps

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:205

Article

Bruti-Liberati, Nicola ; Platen, Eckhard

关键词: jump-diffusion processes;    pure jump processes;    stochastic taylor expansion;    discrete time approximation;    simulation;    strong;    convergence;   

DOI  :  10.1016/j.cam.2006.03.040

来源: Elsevier

【 摘 要 】

This paper is a survey of strong discrete time approximations of jump-diffusion processes described by stochastic differential equations (SDEs). It also presents new results on strong discrete time approximations for the specific case of pure jump SDEs. Strong approximations based on jump-adapted time discretizations, which produce no discretization error in the case of purejump processes, are analyzed. The computational complexity of these approximations is proportional to the jump intensity. By exploiting a stochastic expansion for pure jump processes, higher order discrete time approximations, whose computational complexity is not dependent on the jump intensity, are proposed. For the specific case of pure jump SDEs, the strong order of convergence of strong Taylor schemes is established under weaker conditions than those currently known in the literature. (c) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free