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Rota, Gian-Carlo; Wallstrom, Timothy C.

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

Ann. Probab. 25, No. 3, 1257-1283 (1997).
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.
Reviewer: Gong Guanglu (Beijing)

Cited in 3 Reviews
Cited in 24 Documents

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

Keywords:

multiple stochastic integral; partition of set; discrete and homogeneous chaos; orthogonal polynomial; symmetric function; Kailath-Segall formula
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\textit{G.-C. Rota} and \textit{T. C. Wallstrom}, Ann. Probab. 25, No. 3, 1257--1283 (1997; Zbl 0886.60046)
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