Fields of interest and research
Stochastic analysis and stochastic modeling
Markov chains.
Discrete and continuous time Markov chains, random walk;
application to queues, molecular biology, phylogeny.
Hidden Markovian models; probabilistic study of genome.
Stochastic processes.
Continuous time Markov processes and diffusions, Gaussian processes,
Brownian motion, Ornstein-Uhlenbeck process; application to reliability,
finance. Branching processes; application to genealogy.
Jump processes.
Stable processes, Lévy processes.
Random motions in space.
Hyperbolic Fokker-Planck equations of order higher than 2;
Markovian pseudo-processes associated with heat-type equations of order higher than 2.
Random matrices.
Application to the computation of entropy in quantum physics.
Inference statistics.
Functional estimating, goodness of fit tests (tests of Kolmogorov-Smirnov, Cramér-von Mises-type).
Random simulation.
Simulation of Markov chains and stochastic processes.
Monte-Carlo methods: applications to solving some partial differential equations,
computing some electrical potentials.
Stochastic algorithms.
Simulated annealing, Gibbs sampler. Application to image processing:
rebuilding and restoration of images.
Multivoques stochastic differential equations.
Application to seismology.
Disclosure of Mathematics.
Mathematics and Magic: Card Magic and Numerology.
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