MULTIPLE STRATONOVICH INTEGRAL AND HU-MEYER FORMULA FOR LEVY PROCESSES

• 成果类型: Article
• 署名作者: Farre, Merce; Jolis, Maria; Utzet, Frederic
• 署名单位: Autonomous University of Barcelona
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP528
• 发表日期: 2010
• 页码: 2136-2169
• 关键词: free stochastic-measures; Respect; Poisson

摘要

In the framework of vector measures and the combinatorial approach to stochastic multiple integral introduced by Rota and Wallstrom [Ann. Probab. 25 (1997) 1257-1283], we present an Ito multiple integral and a Stratonovich multiple integral with respect to a Levy process with finite moments up to a convenient order. In such a framework, the Stratonovich multiple integral is an integral with respect to a product random measure whereas the Ito multiple integral corresponds to integrate with respect to a random measure that gives zero mass to the diagonal sets. A general Hu-Meyer formula that gives the relationship between both integrals is proved. As particular cases, the classical Hu-Meyer formulas for the Brownian motion and for the Poisson process are deduced. Furthermore, a pathwise interpretation for the multiple integrals with respect to a subordinator is given.