Abstract
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 Itô multiple integral and a Stratonovich multiple integral with respect to a Lévy 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 Itô 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. © Institute of Mathematical Statistics, 2010.
Original language | English |
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Pages (from-to) | 2136-2169 |
Number of pages | 34 |
Journal | Annals of Probability |
Volume | 38 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1 Nov 2010 |
Keywords
- Hu-Meyer formula
- Lévy processes
- Random measures
- Stratonovich integral
- Teugels martingales