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Coupling polynomial Stratonovich integrals : the two-dimensional Brownian case

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Banerjee, Sayan and Kendall, W. S. (2018) Coupling polynomial Stratonovich integrals : the two-dimensional Brownian case. Electronic Journal of Probability, 23 . 24. doi:10.1214/18-EJP150

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Official URL: https://doi.org/10.1214/18-EJP150

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Abstract

We show how to build an immersion coupling of a two-dimensional Brownian motion (W1,W2) along with (n2)+n=12n(n+1). integrals of the form ∫Wi1Wj2∘dW2, where j=1,…,n and i=0,…,n−j for some fixed n. The resulting construction is applied to the study of couplings of certain hypoelliptic diffusions (driven by two-dimensional Brownian motion using polynomial vector fields). This work follows up previous studies concerning coupling of Brownian stochastic areas and time integrals (Ben Arous, Cranston and Kendall (1995), Kendall and Price (2004), Kendall (2007), Kendall (2009), Kendall (2013), Banerjee and Kendall (2015), Banerjee, Gordina and Mariano (2016)) and is part of an ongoing research programme aimed at gaining a better understanding of when it is possible to couple not only diffusions but also multiple selected integral functionals of the diffusions.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Brownian motion processes, Stochastic differential equations, Diffusion processes, Polynomials
Journal or Publication Title: Electronic Journal of Probability
Publisher: University of Washington. Dept. of Mathematics
ISSN: 1083-6489
Official Date: 27 February 2018
Dates:
DateEvent
27 February 2018Published
2 February 2017Accepted
Volume: 23
Number of Pages: 43
Article Number: 24
DOI: 10.1214/18-EJP150
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/K013939[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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