Equation différentielle anticipative sur une variété et approximations

✍ Scribed by Axel Grorud; Monique Pontier

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 505 KB
• Volume: 38
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/0378-4754(93)e0066-e

✦ Synopsis

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).