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

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  • Russo, Francesco
  • Vallois, Pierre

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.

Suggested Citation

  • Russo, Francesco & Vallois, Pierre, 1998. "Product of two multiple stochastic integrals with respect to a normal martingale," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 47-68, January.
    • Handle: RePEc:eee:spapps:v:73:y:1998:i:1:p:47-68
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    References listed on IDEAS

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    1. Vallois, P., 1995. "Decomposing the Brownian path via the range process," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 211-226, February.
    2. Russo, Francesco & Vallois, Pierre, 1995. "The generalized covariation process and Ito formula," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 81-104, September.
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    Keywords

    60G44 60H05 60H07 60J65;

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