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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
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 | ||||||
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| 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 | ||||||
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| 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: |
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