Advanced Topics in Probability Theory

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ProbStochProcPicture


This course exposes the student to the basic notions of stochastic processes and to the recent applications in financial problems.

Main Topics

Part A

  • Law of large numbers
  • Central limit theorems for Gaussian and Levy distributions, with application to the Random Energy Model
  • Markov processes
  • Chapman Kolmogorv theory
  • Ito calculus
  • Langevin equation
  • Fokker-Planck equation and application

Part B

  • Introduction to game theory and to economic equilibrium
  • Stochastic processes and financial mathematics
  • Application of statistical mechanics to interacting agent systems

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