A combinatorial definition of multiple stochastic integrals is
given in the setting of random measures. It is shown that some properties of
such stochastic integrals, formerly known to hold in special cases, are
instances of combinatorial identities on the lattice of partitions of a set.
The notion of stochastic sequences of binomial type is introduced as a
generalization of special polynomial sequences occuring in stochastic
integration, such as Hermite, Poisson–Charlier and Kravchuk polynomials.
It is shown that identities for such polynomial sets have a common origin.
Publié le : 1997-07-14
Classification:
Multiple stochastic integrals,
partitions of sets,
discrete and homogeneous chaos,
orthogonal polynomials,
symmetric functions,
Kailath-Segall formula,
60H05,
05A18,
05E05,
05E35,
11B65,
60G57,
81T18
@article{1024404513,
author = {Rota, Gian-Carlo and Wallstrom, Timothy C.},
title = {Stochastic integrals: a combinatorial approach},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1257-1283},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404513}
}
Rota, Gian-Carlo; Wallstrom, Timothy C. Stochastic integrals: a combinatorial approach. Ann. Probab., Tome 25 (1997) no. 4, pp. 1257-1283. http://gdmltest.u-ga.fr/item/1024404513/