1. Conditionally Gaussian stochastic integrals.
- Author
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Privault, Nicolas and She, Qihao
- Subjects
- *
GAUSSIAN processes , *STOCHASTIC integrals , *IDENTITIES (Mathematics) , *MATHEMATICAL forms , *MALLIAVIN calculus , *MATRICES (Mathematics) , *FUNCTIONALS , *CHARACTERISTIC functions - Abstract
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]
- Published
- 2015
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