Contenido
- Basic stochastic processes: Stochastic processes, Markov chains, martingales.
- Small noise exit for Brownian motion and diffusions: Schilder’s theorem, Diffusion with additive noise, LDP for diffusions, First exit form the domain, Connection to eigenvalues, Metastability, Application: Stochastic resonance, Application: Simulated annealing.
- Small noise exit for heavy tail Lévy processes and jump diffusions: Heavy tails, stable, tempered stable LP, One jump principle, First exit for Lévy-driven jump diffusion, Metastability, Connection to eigenvalues, Application: Stochastic resonance, Application: Simulated annealing.
- Wong–Zakai approximations: Approximation theorem for BM and Brownian SDE, Lamperti transformation, Linear Langevin equation with Lévy noise, Skorohod topologies J 1 and M 1, Marcus SDEs, Advection-diffusion equation with Lévy noise on the boundary.