Stochastic Differential Equations

1 Unit · Graduate

Brownian motion and Langevin's equation. Ito and Stratonovich stochastic integrals. Stochastic calculus and Ito's formula. SDEs and PDEs of Kolmogorov, Fokker-Planck, and Dynkin. Boundary conditions, exit times, exit distributions, stability. Asymptotic analysis of SDE, the Smoluchowski-Kramers approximation, and diffusion approximation to Markov chains. Applications.