Search

We derive conditional Gaussian type identities of the form E [ exp ⁡ ( i ∫ 0 T u t d B t ) | ∫ 0 T | u t | 2 d t ] = exp ⁡ ( − 1 2 ∫ 0 T | u t | 2 d t ) , for Brownian stochastic integrals, under conditions on the process ( u t ) t ∈ [ 0 , T ] specified using the Malliavin calculus. This applies in particular to the quadratic Brownian integral ∫ 0 t A B s d B s under the matrix condition A † A 2 = 0 , using a characterization of Yor [6] . [ABSTRACT FROM AUTHOR]

Abstract: We propose a formula for the computation of the moments of all orders of Itô and Skorohod stochastic integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. Some characterizations of Gaussian distributions for stochastic integrals are recovered as a consequence. [Copyright &y& Elsevier]