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Title: Backward doubly stochastic differential equations with polynomial growth coefficients
Authors: Zhang, Qi
Zhao, Huaizhong
Keywords: Backward doubly stochastic differential equations
Polynomial growth coefficients
SPDEs
Malliavin derivative
Wiener-Sobolev compactness
Issue Date: 2015
Publisher: © American Institute of Mathematical Sciences
Citation: ZHANG, Q. and ZHAO, H., 2015. Backward doubly stochastic differential equations with polynomial growth coefficients. Discrete and Continuous Dynamical Systems, Series A, 35 (11), pp.5285-5315.
Abstract: In this paper we study the solvability of backward doubly stochastic differential equations (BDSDEs for short) with polynomial growth coeffi-cients and their connections with SPDEs. The corresponding SPDE is in a very general form, which may depend on the derivative of the solution. We use Wiener-Sobolev compactness arguments to derive a strongly convergent subsequence of approximating SPDEs. For this, we prove some new estimates to the solution and its Malliavin derivative of the corresponding approximating BDSDEs. These estimates lead to the verifications of the conditions in the Wiener-Sobolev compactness theorem and the solvability of the BDSDEs and the SPDEs with polynomial growth coefficients.
Description: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems, Series A following peer review. The definitive publisher-authenticated version ZHANG, Q. and ZHAO, H., 2015. Backward doubly stochastic differential equations with polynomial growth coefficients. Discrete and Continuous Dynamical Systems, Series A, 35 (11), pp.5285-5315. is available online at: http://dx.doi.org/10.3934/dcds.2015.35.5285
Version: Accepted for publication
DOI: 10.3934/dcds.2015.35.5285
URI: https://dspace.lboro.ac.uk/2134/21237
Publisher Link: http://dx.doi.org/10.3934/dcds.2015.35.5285
ISSN: 1078-0947
Appears in Collections:Published Articles (Maths)

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