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11. Mixing of Poisson random measures under interacting transformations.

Author

Privault, Nicolas

Subjects
*POISSON processes, *RANDOM measures, *MATHEMATICAL transformations, *MIXING, *MALLIAVIN calculus, *MEASURE theory
Abstract

We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical result in the case of deterministic transformations of Poisson measures. The approach relies on moment and covariance identities for Poisson stochastic integrals with random integrands. [ABSTRACT FROM PUBLISHER]

Published
2016
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12. Conditional Stein approximation for Itô and Skorohod integrals.

Author

Privault, Nicolas and She, Qihao

Subjects
*MALLIAVIN calculus, *EDGEWORTH expansions, *STOCHASTIC integrals, *BROWNIAN motion, *LAPLACE transformation
Abstract

We derive conditional Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain conditional Stein approximation bounds for multiple stochastic integrals and quadratic Brownian functionals. [ABSTRACT FROM AUTHOR]

Published
2017
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