34 citations · 43 across the 9 of their papers we have counts for
13 papers
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…
Estimation of the average number of continuous crossings for non-stationary non-diffusion processes
Romain Azaïs, Alexandre Genadot
Assume that you observe trajectories of a non-diffusive non-stationary process and that you are interested in the average number of times where the process crosses some threshold (…
Inference for conditioned Galton-Watson trees from their Harris path
Romain Azaïs, Alexandre Genadot, Benoît Henry
Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML…
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…
A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions
Romain Azaïs, Alexandre Genadot
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In t…
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…
Piecewise deterministic Markov process - recent results
Romain Azaïs, Jean-Baptiste Bardet, Alexandre Genadot +2
We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these proc…
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…