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Stochastic integrals: A combinatorial approach. (English) Zbl 0886.60046

A unified combinatorial definition of multiple stochastic integrals is given in the setting of random measures. The notion of stochastic sequence of binomial type is introduced as a generalization of special polynomial sequences appearing commonly in stochastic integration including Hermite, Poisson-Charlier and Kravchuk polynomials.

MSC:

60H05 Stochastic integrals
05E05 Symmetric functions and generalizations
05E35 Orthogonal polynomials (combinatorics) (MSC2000)
11B65 Binomial coefficients; factorials; \(q\)-identities
60G57 Random measures
81T18 Feynman diagrams
05A18 Partitions of sets
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