This course introduces the main notions of probability concerning the study of continuous-time processes. In particular, it develops the theory of stochastic differential equations and diffusions and that of jump processes. Most of the examples will be drawn from applications in biology. The main parts of the course will be as follows.
Continuous-time processes
Markov processes
Continuous-time martingales, stopping time
Brownian motion and stochastic calculus
Stochastic differential equations
Pure jump processes and Poisson point measures,
Continuous time branching processes and birth and death processes,
Limit theorems. Applications to continuous approximations of jump processes.
- Teaching coordinator: Méléard Sylvie