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ES_APPM 442-0: Stochastic Differential Equations

Description

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, diffusion approximation to Markov chains. Applications.