This course starts from reviewing  the basic probability theory and stochastic processes such as Markov chains, Poisson processes and so on, and then studies Brownian motions, Ito formula, Ornstein-Uhlenbeck process, growth models, Black-Scholes equations and some applications of stochastic differential equations in Finance and biology.

CILO-1: Identify the key points of Brownian motion, continuous semimartingales and Markov processes. CILO-2: Demonstrate the construction of stochastic integrals with respect to semimartingales. CILO-3: Apply Ito’s formula and consequences to the study of stochastic differential equations.