34 citations · 43 across the 9 of their papers we have counts for
9 papers · 1 filter
A convex programming approach for discrete-time Markov decision processes under the expected total reward criterion
F. Dufour, Alexandre Genadot
In this work, we study discrete-time Markov decision processes (MDPs) under constraints with Borel state and action spaces and where all the performance functions have the same for…
On the expected total reward with unbounded returns for Markov decision processes
François Dufour, Alexandre Genadot
We consider a discrete-time Markov decision process with Borel state and action spaces. The performance criterion is to maximize a total expected {utility determined by unbounded r…
Probabilistic and Piecewise Deterministic models in Biology
Bertrand Cloez, Renaud Dessalles, Alexandre Genadot +3
We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by Davis (19…
Averaging for some simple constrained Markov processes
Alexandre Genadot
In this paper, a class of piecewise deterministic Markov processes with underlying fast dynamic is studied. Using a "penalty method" , an averaging result is obtained when the unde…
Simulation of SPDE's for Excitable Media using Finite Elements
Boulakia Muriel, Genadot Alexandre, Thieullen Michèle
In this paper, we address the question of the discretization of Stochastic Partial Differential Equations (SPDE's) for excitable media. Working with SPDE's driven by colored noise,…
A multi-scale study of a class of hybrid predator-prey models
Alexandre Genadot
We address the question of an averaging principle for a general class of multi-scale hybrid predator-prey models. We consider prey-predator models where the kinetic of the prey pop…
Spatio-temporal averaging for a class of hybrid systems. Application to conductance-based neuron models
Alexandre Genadot
We obtain a limit theorem endowed with quantitative estimates for a general class of infinite dimensional hybrid processes with intrinsically two different time scales and includin…
Multiscale Piecewise Deterministic Markov Process in Infinite Dimension: Central Limit Theorem and Langevin Approximation
A. Genadot, M. Thieullen
In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on a…
Averaging for a Fully-Coupled Piecewise Deterministic Markov Process in Infinite Dimension
Alexandre Genadot, Michèle Thieullen
In this paper, we consider the generalized Hodgkin-Huxley model introduced by Austin in \cite{Austin}. This model describes the propagation of an action potential along the axon of…