MULTIPLE STRATONOVICH INTEGRAL AND HU-MEYER FORMULA FOR LEVY PROCESSES

作者：Farre Merce^*; Jolis Maria; Utzet Frederic

来源：Annals of Probability, 2010, 38(6): 2136-2169.

DOI：10.1214/10-AOP528

• Levy processes
• Stratonovich integral
• Hu-Meyer formula
• random measures
• Teugels martingales

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.

• 出版日期2010-11