Imperial College London
Portrait Picture

Professor Xue-Mei Li

Faculty of Natural Sciences, Department of Mathematics

Chair in Probability and Stochastic Analysis
 
 
 
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Contact

 

+44 (0)20 7594 3709xue-mei.li Website CV

 
 
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Location

 

6M51Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@inbook{Li:2018:10.1007/978-3-030-01593-0_18,
author = {Li, X-M},
booktitle = {Computation and Combinatorics in Dynamics, Stochastics and Control},
doi = {10.1007/978-3-030-01593-0_18},
editor = {Celledoni and Di, Nunno and Ebrahimi-Fard and Munthe-Kaas},
pages = {499--550},
publisher = {Springer},
title = {Perturbation of conservation laws and averaging on manifolds},
url = {http://dx.doi.org/10.1007/978-3-030-01593-0_18},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - CHAP
AB  - We prove a stochastic averaging theorem for stochastic differential equations in which the slow and the fast variables interact. The approximate Markov fast motion is a family of Markov process with generator Lx for which we obtain a quantitative locally uniform law of large numbers and obtain the continuous dependence of their invariant measures on the parameter x. These results are obtained under the assumption that Lx satisfies Hörmander’s bracket conditions, or more generally Lx is a family of Fredholm operators with sub-elliptic estimates. For stochastic systems in which the slow and the fast variable are not separate, conservation laws are essential ingredients for separating the scales in singular perturbation problems we demonstrate this by a number of motivating examples, from mathematical physics and from geometry, where conservation laws taking values in non-linear spaces are used to deduce slow-fast systems of stochastic differential equations.
AU  - Li,X-M
DO  - 10.1007/978-3-030-01593-0_18
EP  - 550
PB  - Springer
PY  - 2018///
SN  - 978-3-030-01592-3
SP  - 499
TI  - Perturbation of conservation laws and averaging on manifolds
T1  - Computation and Combinatorics in Dynamics, Stochastics and Control
UR  - http://dx.doi.org/10.1007/978-3-030-01593-0_18
UR  - http://arxiv.org/abs/1705.08857v1
UR  - https://www.springer.com/gp/book/9783030015923
UR  - http://hdl.handle.net/10044/1/92353
ER  -
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