UNADAPTED STOCHASTIC CALCULUS FOR 2-PARAMETER PROCESSES - STRATONOVICH AND SKOROHOD CHANGE OF VARIABLE FORMULAS

• 成果类型: Article
• 署名作者: THIEULLEN, M
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01199789
• 发表日期: 1991
• 页码: 457-485
• 关键词: integrals; martingales

摘要

We prove a Stratonovitch-type change of variable formula for anticipative processes on [0, 1]2. The formula is the same as the existing one from deterministic calculus. In order to do so we define simple and double Stratonovitch integrals. We deduce a Skorohod-type change of variable formula which does not contain any line integral. Our method consists in using regularization of the Wiener process obtained by convolution.