Multiple Stochastic Integrals via Sequences in Geometric Algebras
نویسنده
چکیده
A combinatorial construction of the multiple stochastic integral is developed using sequences in Clifford (geometric) algebras. In particular, sequences of Berezin integrals in an ascending chain of geometric algebras converge in mean to the iterated stochastic integral. By embedding such chains within an infinite-dimensional Clifford algebra, an infinitedimensional analogue of the Berezin integral is discovered. Hermite and Poisson-Charlier polynomials are recovered as limits of Berezin integrals using this construction.
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