UE Stochastic processes



  1. Conditional expectation
  2. General information on discrete time stochastic processes
    • Construction, canonical space, filtrations, downtime
  3. Martingales in discrete time
    • Theorems of arrest, convergence theorems, regular martingales (see note), applications (player's ruin, Galton-Watson process, etc.)
  4. Markov chains with finite or countable state space
    • Algebraic and probabilistic aspects, Markov property, classification of states, recurrence, transience, periodicity, stationary laws, ergodic theorem (in the positive recurrent case), convergence to stationary law, examples and applications (diffusion models, genetic models, waiting lines, etc.)

Note: The time allotted does not allow for demonstration of the convergence theorem of the martingales, except in the case of integrable square, nor to fully characterize the regular martingales.


The parts devoted to the probabilities of Measurement theory, introduction to probabilities in L3A and the Statistics course in the first half of the first year Master's.


  • Philippe Barbe, Michel Ledoux, Probabilité L3-M1, EDP Sciences 2007
  • Laurent Mazliak, Pierre Priouret, Paolo Baldi, Martingales et chaînes de Markov, Hermann 1998
  • Djalil Chafaï, Florent Malrieu, Recueil de Modèles Aléatoires, Springer 2016, également disponible sur HAL



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