Imperial College London
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ProfessorDanCrisan

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8489d.crisan Website

 
 
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Location

 

670Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Crisan:2015:10.1016/j.jfa.2014.12.009,
author = {Crisan, D and Litterer, C and Lyons, T},
doi = {10.1016/j.jfa.2014.12.009},
journal = {Journal of Functional Analysis},
pages = {1928--1971},
title = {Kusuoka-Stroock gradient bounds for the solution of the filtering equation},
url = {http://dx.doi.org/10.1016/j.jfa.2014.12.009},
volume = {268},
year = {2015}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock [13,14,16,17], and extends their program developed for the heat semi-group to solutions of stochastic partial differential equations. The work is motivated by and applied to nonlinear filtering. The analysis allows us to derive pathwise gradient bounds for the un-normalised conditional distribution of a partially observed signal. It uses a pathwise representation of the perturbed semigroup following Ocone [22]. The estimates we derive have sharp small time asymptotics.
AU  - Crisan,D
AU  - Litterer,C
AU  - Lyons,T
DO  - 10.1016/j.jfa.2014.12.009
EP  - 1971
PY  - 2015///
SN  - 0022-1236
SP  - 1928
TI  - Kusuoka-Stroock gradient bounds for the solution of the filtering equation
T2  - Journal of Functional Analysis
UR  - http://dx.doi.org/10.1016/j.jfa.2014.12.009
UR  - http://hdl.handle.net/10044/1/30611
VL  - 268
ER  -
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