Geodesic
Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes
Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 61-83

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The paper deals with problems of constructing multiple stochastic integrals in the case when the product of increments of the integrating stochastic process admits an expansion as a finite sum of series with random coefficients. This expansion was obtained for a sufficiently wide class including centered Gaussian processes. In the paper, some necessary and sufficient conditions are obtained for the existence of multiple stochastic integrals defined by an expansion of the product of Wiener processes. It was obtained a recurrent representation for the Wiener stochastic integral as an analog of the Hu–Meyer formula. 
@article{MT_2014_17_2_a3,
     author = {I. S. Borisov and S. E. Khrushchev},
     title = {Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes},
     journal = {Matemati\v{c}eskie trudy},
     pages = {61--83},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2014_17_2_a3/}
}
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I. S. Borisov; S. E. Khrushchev. Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes. Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 61-83. http://geodesic.mathdoc.fr/item/MT_2014_17_2_a3/