arXiv subjects

Brice Samegni-Kepgnou

Publications and source records attributed to Brice Samegni-Kepgnou.

3 recordsLinked to original sources

arXiv2018

Large Deviations of the Exit Measure through a Characteristic Boundary for a Poisson driven SDE

Let O the basin of attraction of the unique stable equilibrium of a dynamical system, which is the law of large numbers limit of a Poissonian SDE. We consider the law of the exit point from O of that Poissonian SDE. We adapt the approach of M. Day (1990) for the same problem for a Brownian SDE. For that purpose, we will use the Large deviation for the Poissonian SDE reflected at the boundary of O studied in our recent work Pardoux and Samegni (2018).

math.PR↗

arXiv2018

Large Deviation Principle for Reflected Poisson driven SDEs in Epidemic Models

We establish a large deviation principle for a reflected Poisson driven SDE. Our motivation is to study in a forthcoming paper the problem of exit of such a process from the basin of attraction of a locally stable equilibrium associated with its law of large numbers. Two examples are described in which we verify the assumptions that we make to establish the large deviation principle.

math.PR↗

arXiv2016

Large deviation principle for Poisson driven SDEs in epidemic models

We consider a general class of epidemic models obtained by applying a random time change to a collection of Poisson processes and we show the large deviation principle for such models. We generalize to a more general situation the approach followed by Dolgoaschinnykh [3] in the case of the SIR epidemic model. Thanks to an assumption which is satisfied in many examples, we simplify the recent work by P. Kratz and E. Pardoux [8].

math.PR↗