Multiple Stochastic Integrals via Sequences in Geometric Algebras

A combinatorial construction of the multiple stochastic integral is de-veloped using sequences in Clifford (geometric) algebras. In particular, sequences of Berezin integrals in an ascending chain of geometric alge-bras converge in mean to the iterated stochastic integral. By embedding such chains within an infinite-dimensional Clifford algebra, an infinite-dimensional analogue of the Berezin integral is discovered. Hermite and Poisson-Charlier polynomials are recovered as limits of Berezin integrals using this construction.