AN OPERATOR APPROACH FOR MARKOV CHAIN WEAK APPROXIMATIONS WITH AN APPLICATION TO INFINITE ACTIVITY LEVY DRIVEN SDES

• 成果类型: Article
• 署名作者: Tanaka, Hideyuki; Kohatsu-Higa, Arturo
• 署名单位: Mitsubishi International Corporation (MIC); University of Osaka
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP568
• 发表日期: 2009
• 页码: 1026-1062
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; euler scheme; error

摘要

Weak approximations have been developed to calculate the expectation value of functionals of stochastic differential equations, and various numerical discretization schemes (Euler, Milshtein) have been studied by many authors. We present a general framework based on semigroup expansions for the construction of higher-order discretization schemes and analyze its rate of convergence. We also apply it to approximate general Levy driven stochastic differential equations.