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Averaging for slow–fast piecewise deterministic Markov processes with an attractive boundary

Part of: Limit theorems Markov processes Stochastic analysis

Published online by Cambridge University Press:  19 May 2023

Alexandre Génadot
Alexandre Génadot*
Affiliation:
Univ. Bordeaux, CNRS, INRIA, Bordeaux INP, IMB, UMR 5251
*
*Postal address: Univ. Bordeaux, CNRS, INRIA, Bordeaux INP, IMB, UMR 5251, 33400 Talence, France. Email address: alexandre.genadot@u-bordeaux.fr
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Abstract

In this paper we consider the problem of averaging for a class of piecewise deterministic Markov processes (PDMPs) whose dynamic is constrained by the presence of a boundary. On reaching the boundary, the process is forced to jump away from it. We assume that this boundary is attractive for the process in question in the sense that its averaged flow is not tangent to it. Our averaging result relies strongly on the existence of densities for the process, allowing us to study the average number of crossings of a smooth hypersurface by an unconstrained PDMP and to deduce from this study averaging results for constrained PDMPs.

Keywords

Constrained Markov processmultiscale modellingsingular perturbationnumber of crossings

MSC classification

Primary: 60F99: None of the above, but in this section
Secondary: 60H99: None of the above, but in this section 60J99: None of the above, but in this section
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 4 , December 2023 , pp. 1439 - 1468
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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