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Gaussian Approximations of Small Noise Diffusions in Kullback-Leibler Divergence

Sanz-Alonso, Daniel and Stuart, Andrew M. (2017) Gaussian Approximations of Small Noise Diffusions in Kullback-Leibler Divergence. Communications in Mathematical Sciences, 15 (7). pp. 2087-2097. ISSN 1539-6746. doi:10.4310/CMS.2017.v15.n7.a13.

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We study Gaussian approximations to the distribution of a diffusion. The approximations are easy to compute: they are defined by two simple ordinary differential equations for the mean and the covariance. Time correlations can also be computed via solution of a linear stochastic differential equation. We show, using the Kullback–Leibler divergence, that the approximations are accurate in the small noise regime. An analogous discrete time setting is also studied. The results provide both theoretical support for the use of Gaussian processes in the approximation of diffusions, and methodological guidance in the construction of Gaussian approximations in applications.

Item Type:Article
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Additional Information:© 2017 International Press. Received 19 May 2016; Accepted 30 September 3016; Published 16 October 2017. DS-A is supported by EPSRC as part of the MASDOC DTC at the University of Warwick with grant No. EP/H023364/1. The work of AMS is supported by DARPA, EPSRC and ONR.
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/H023364/1
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Subject Keywords:Gaussian approximations, diffusion processes, small noise, Kullback-Leibler divergence
Issue or Number:7
Classification Code:2010 AMS subject classifications. 28C20, 60G15, 60H10, 65L05
Record Number:CaltechAUTHORS:20161220-181911579
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73039
Deposited By: Linda Taddeo
Deposited On:21 Dec 2016 18:35
Last Modified:11 Nov 2021 05:10

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