Discrete processes

Ects : 8

Enseignant responsable :

Volume horaire : 79

Description du contenu de l'enseignement :

  • Conditional expectation: definition and construction, properties
  • Processes: filtrations, stopping times, sigma-field of the past
  • Martingales: definition, stopping theorems, convergence theorems, maximal inequalities
  • Markov chains: definition, random inductions, properties, Markov properties, recurrence and transience, invariant measures, ergodic theory

Compétence à acquérir :

Discrete-time stochastic processes, including conditional expectation, martingales, and Markov chains and their long-term behavior.