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On the combinatorics of iterated stochastic integrals

Jamshidian, Farshid (2008): On the combinatorics of iterated stochastic integrals.

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Abstract

This paper derives several identities for the iterated integrals of a general semimartingale. They involve powers, brackets, exponential and the stochastic exponential. Their form and derivations are combinatorial. The formulae simplify for continuous or finite-variation semimartingales, especially for counting processes. The results are motivated by chaotic representation of martingales, and a simple such application is given.

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