Equation différentielle anticipative sur une variété et approximations

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• 作者：Grorud ; Axel ; Pontier ; Monique
• 关键词：Malliavin derivative ; Second-order geometry ; Skorohod integral ; Stochastic calculus ; Anticipating stochastic differential equation
• 刊名：Mathematics and Computers in Simulation
• 出版年：1995
• 出版时间：May, 1995
• 年：1995
• 卷：38
• 期：1-3
• 页码：51-61
• 全文大小：421 K

文摘

This paper is the sequel of a paper by the authors (1993) and it has a complete version in (1995). We develop a stochastic calculus which allows to integrate non-adapted processes taking their values in the space of second-order 1-forms that are above a manifold valued anticipating process. Using that integration, we study the existence and uniqueness of solution of an anticipating stochastic differential equation in a manifold. This stochastic calculus uses both second-order geometry defined by P.-A. Meyer (1981) and Nualart-Pardoux's duality definition of Skorohod integral (1988).