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Title: Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates
Authors: Privault, Nicolas
Yam, Phillip S. C.
Zhang, Zheng
Keywords: Science::Mathematics
Issue Date: 2019
Source: Privault, N., Yam, P. S. C. & Zhang, Z. (2019). Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates. Stochastic Processes and Their Applications, 129(9), 3376-3405.
Project: MOE2016-T2-1-036
Journal: Stochastic Processes and their Applications
Abstract: This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity λ>0. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of O(λ ) for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.
ISSN: 0304-4149
DOI: 10.1016/
Schools: School of Physical and Mathematical Sciences 
Rights: © 2018 Elsevier B.V. All rights reserved. This paper was published in Stochastic Processes and their Applications and is made available with permission of Elsevier B.V.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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