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Ergodicity of Dissipative Differential Equations Subject to Random Impulses

Sanz-Serna, J. M. and Stuart, A. M. (1999) Ergodicity of Dissipative Differential Equations Subject to Random Impulses. Journal of Differential Equations, 155 (2). pp. 262-284. ISSN 0022-0396. doi:10.1006/jdeq.1998.3594.

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Differential equations subject to random impulses are studied. Randomness is introduced both through the time between impulses, which is distributed exponentially, and through the sign of the impulses, which are fixed in amplitude and orientation. Such models are particular instances of piecewise deterministic Markov processes and they arise naturally in the study of a number of physical phenomena, particularly impacting systems. The underlying deterministic semigroup is assumed to be dissipative and a general theorem which establishes the existence of invariant measures for the randomly forced problem is proved. Further structure is then added to the deterministic semigroup, which enables the proof of ergodic theorems. Characteristic functions are used for the case when the deterministic component forms a damped linear problem and irreducibility measures are employed for the study of a randomly forced damped double-well nonlinear oscillator with a gradient structure.

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Additional Information:© 1999 Academic Press. Received 1 December 1997, Revised 12 June 1998, Available online 1 April 2002. Supported by project PB95-705. Supported by the Office of Naval Research under Grant N00014-92-J-1876. Most of this research was performed while this author was Iberdrola Visiting Professor at Valladolid.
Funding AgencyGrant Number
Universidad de ValladolidPB95-705
Office of Naval Research (ONR)N00014-92-J-1876
Subject Keywords:random impulses; stochastic differential equations; dissipative systems; gradient systems; nonlinear oscillators; ergodic theorem
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ42
Issue or Number:2
Record Number:CaltechAUTHORS:20170609-124028394
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Official Citation:J.M Sanz-Serna, A.M Stuart, Ergodicity of Dissipative Differential Equations Subject to Random Impulses, Journal of Differential Equations, Volume 155, Issue 2, 1999, Pages 262-284, ISSN 0022-0396, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78059
Deposited By: Tony Diaz
Deposited On:09 Jun 2017 21:15
Last Modified:15 Nov 2021 17:36

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