STOCHASTIC INTEGRALS - A COMBINATORIAL APPROACH

A combinatorial definition of multiple stochastic integrals is given i n the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, ar e instances of combinatorial identities on the lattice of partitions o f a set. The notion of stochastic sequences of binomial type is introd uced as a generalization of special polynomial sequences occuring in s tochastic integration, such as Hermite, Poisson-Charlier and Kravchuk polynomials. It is shown that identities for such polynomial sets have a common origin.