Chaotic Kabanov formula for the Azéma martingales

Nicolas Privault, Josep Lluís Solé, and Josep Vives

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We derive the chaotic expansion of the product of nth- and first-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integrals, polynomials and Wick products, that characterize the Wiener and Poisson processes.

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Bernoulli Volume 6, Number 4 (2000), 633-651.

First available in Project Euclid: 8 April 2004

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Azéma martingales multiple stochastic integrals product formulae


Privault, Nicolas; Lluís Solé, Josep; Vives, Josep. Chaotic Kabanov formula for the Azéma martingales. Bernoulli 6 (2000), no. 4, 633--651.

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