Product of two multiple stochastic integrals with respect to a normal martingale

Francesco Russo and Pierre Vallois

Stochastic Processes and their Applications, 1998, vol. 73, issue 1, 47-68

Abstract: Let M be a normal martingale (i.e. (t) = t), we decompose the product of two multiple stochastic integrals (with respect to M) In(f)Im(g) as a sum of n [logical and] m terms Hk. Hk is equal to the integral over k+ of the function t --> In+m-2k(hk(t,.)), with respect to the k-tensor product of d[M,M]., hk being an explicit function depending only on f and g. Our formula generalizes the well-known result concerning Brownian motion and compensated Poisson process and allows us to improve some results of Emery related to the chaos representation property of solution of the structure equation.

Keywords: 60G44; 60H05; 60H07; 60J65 (search for similar items in EconPapers)
Date: 1998
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