Research

Research interests

Among applied mathematics, I am interested in:

• Piecewise deterministic processes
  • Averaging
  • Optimal stochastic control
  • Statistical inference
• Statistics for linguistics
  • database design
  • diatopic variation modelization

Work in progress

• About Fisher Information Matrix and Self-Optimizing Control in Bearing Only Localization
  with E. Iglésis and L. de Montella.
• The Bearing Only Localization Problem via Partially Observed Markov Decision Process
  with F. Dufour and R. Namyst.
• Non-Stationary Value Iteration Adaptive Average Control for Piecewise Deterministic Markov Processes
  with F. Dufour and O. Costa.
• Preface for the new edition of the book Los Secrets written by a paludèir from Bègles, new edition edited by D. Escarpit, published by Per Noste.

Papers

• Adaptive Average Control for Piecewise Deterministic Markov Processes
  with F. Dufour and O. Costa
  Systems & Control Letters
  Volume 192, 2024, SCL
• Minimum Contrast Estimators for Piecewise Deterministic Markov Processes
  with F. Dufour and O. Costa
  Numerical Algebra, Control and Optimization
  2024, NACO
• Which methodology to analyse the Bourciez survey?
  2023, Lengas
  
• Averaging for slow-fast piecewise deterministic Markov processes with an attractive boundary
  HAL preprint
  2022, AAP
  
• A convex programming approach for discrete-time Markov decision processes under the expected total reward criterion
  with F. Dufour
  SIAM Journal on Control and Optimization
  Volume 58(4), 2020, SICON
• Self-similar behaviour of a non-local diffusion equation with time delay
  with A. Ducrot
  SIAM Journal on Mathematical Analysis
  Volume 53(3), 2020, SIMA
• On the expected total cost with unbounded returns for Markov decision processes
  with F. Dufour
  Applied Mathematics & Optimization
  Volume 82, 2020 AMO
• Estimation of the average number of continuous crossings for non-stationary non-diffusion processes
  with R. Azaïs
  Journal of Statistical Planning and Inference
  Volume 198, 2019, JSPI
• Inference for conditioned Galton-Watson trees from their Harris path
  with R. Azaïs and B. Henry
  Revista Latino-Americana de Probabilidade e Estatística
  Volume 16, 2019, ALEA
  A Matlab toolbox associated to this paper is available here
• Averaging for some simple constrained Markov processes
  Probability and Mathematical Statistics
  Volume 39(1), 2019, PMS
• A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions
  with R. Azaïs
  Communications in Statistics: Theory and Methods
  Volume 47(8), 2018, CS:TM
• Probabilistic and Piecewise Deterministic models in Biology
  with B. Cloez, R. Dessalles, F. Malrieu, A. Marguet and R. Yvinec
  ESAIM: Proceedings and Surveys
  Volume 60, 2017, ESAIM:PS
• Spatio-temporal averaging for a class of hybrid systems
  Nonlinear Analysis: Hybrid Systems
  Volume 22, 2016, NA:HS
• Simulations of Stochastic Partial Differential Equations for Excitable Media using Finite Elements
  with M. Boulakia and M. Thieullen
  Journal Of Scientific Computing
  Volume 65(1), 2015. JSC
• Semi-parametric inference for the absorption features of a growth-fragmentation model with R. Azaïs
  TEST
  Volume 24(2), 2015, TEST
• Piecewise Deterministic Markov Process (PDMPs). Recent Results
  with R. Azaïs, J-B. Bardet, N. Krell and P-A. Zitt
  ESAIM: Proceedings and Surveys
  Volume 44, 2014, ESAIM:PS
• Multiscale Piecewise Deterministic Markov Process in Infinite Dimension: Central Limit Theorem and Langevin Approximation
  with M. Thieullen
  ESAIM: Probability and Statistics
  Volume 18, 2014, ESAIM:PS
• Averaging for a fully coupled Piecewise Deterministic Markov Process in Infinite Dimensions
  with M. Thieullen
  Advances in Applied Probability
  Volume 44(3), 2012, AAP

Chapter

• Level Crossings and Absorption of an Insurance Model
  with R. Azaïs
  In Statistical Inference for Piecewise-deterministic Markov Processes
  Edited by F. Bouguet and R. Azaïs, Wiley
  Volume 44(3), 2018

HDR

• Contributions à l’étude des processus markoviens déterministes par morceaux et de décision ainsi qu’à l’étude de l’enquête Bourciez
  2023, HDR

Unpublished note

• A multi-scale study of a class of hybrid predator-prey models
  2014, Arxiv