Teaching
Lectures (hand-written) given at Santiago do Chile in November 2025: the first five lectures concern finite state spaces and the last one is an introduction by analogy to diffusion processes.
Markov processes (lecture 1: Markov generators)
Markov processes (lecture 2: semigroups)
Markov processes (lecture 3: spectral gap)
Markov processes (lecture 4: relative entropy)
Markov processes (lecture 5: simulated annealing)
Markov processes (lecture 6: diffusion processes)
Mini-lectures given at the conference Intertwining between Probability, Analysis and Statistical Physics at Singapore in August 5-15, 2024.
On set-valued intertwining duality for diffusion processes (lecture 1)
On set-valued intertwining duality for diffusion processes (lecture 2)
On set-valued intertwining duality for diffusion processes (lecture 3)
On set-valued intertwining duality for diffusion processes (lecture 4)
Mini-lectures given at the meeting of the ANR Stab which took place at Paris in November 25-27, 2015.
On links between quantitative ergodicity and absorption
The draft (hand-written) of the lectures given at the IFCAM Summer School in Bangalore (India) in July 2014. They presented stochastic some algorithms finding Fréchet means on Riemannian manifolds (joint work with Marc Arnaudon), as well as the principles of simulated annealing on which they are based.
On the convergence of stochastic algorithms
All the structural preliminaries (except French) needed about finite time-inhomogeneous Markov processes before working more seriously with them: Markov property, canonical set of trajectories, generators, semi-groups, invariant and reversible measures, martingale problems, Girsanov’s type transformations, probabilistic construction, the example of generalized simulated annealing etc.
Processus de Markov inhomogènes finis