Samuel HERRMANN

Professeur de Mathématiques Appliquées à l’université de Bourgogne
membre de l’équipe Statistique, Probabilités et Applications
membre extérieur de l’équipe projet TOSCA de l’INRIA


Simulation of stochastic processes (Master in Turin)
  1. Chapter 1: Simulation of random variables
    2. 1. Random number generators
    2. Classical discrete random variables
    3. Continuous random variables (reciprocal function and acceptance/rejection methods)

    Exercises and Python file (jupyter notebook)

  2. Chapter 2: Monte Carlo methods
    3. 1. Rejection method (Hit or miss)
    2. Sample mean method
    3. Variance reduction techniques

    Exercises and Python file (jupyter notebook)

  3. Chapter 3: Simulation of a Brownian motion
    4. 1. Properties and definition
    2. Simulation of 1-dimensional binomial
    - As a Gaussian processes
    - Using Lévy's argument (Brownian bridge)
    - Karhunen-Loève theorem
    3. Simulation of a d-dimensional Brownian motion, a Q-Brownian motion

    Exercises and Python file (jupyter notebook)

  4. Chapter 4: Stochastic differential equations (SDE) - définition and simulation
    5. 1. Introduction: deterministic IVP
    2. Stochastic integration
    3. Euler and Milstein schemes
    4. Exact simulation method