Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 2: 305 - 320

DOI: https://doi.org/10.1007/s11464-012-0193-6

RESEARCH ARTICLE

Strong convergence rate of principle of averaging for jump-diffusion processes

  • Di LIU
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  • Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Received date: 16 Jan 2011

Accepted date: 06 Sep 2011

Published date: 01 Apr 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We study jump-diffusion processes with two well-separated time scales. It is proved that the rate of strong convergence to the averaged effective dynamics is of order O(ϵ1/2), where ϵ≪1 is the parameter measuring the disparity of the time scales in the system. The convergence rate is shown to be optimal through examples. The result sheds light on the designing of efficient numerical methods for multiscale stochastic dynamics.

Key words： Stochastic differential equation; time scale separation; averaging of perturbations

Cite this article

Di LIU . Strong convergence rate of principle of averaging for jump-diffusion processes[J]. Frontiers of Mathematics in China, 2012 , 7(2) : 305 -320 . DOI: 10.1007/s11464-012-0193-6

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