1. Conditional expectation, conditional probability, and convergences of random variables. 2. Poisson process and compound Poisson process. 3. Markov chain and Markov processes. 4. Stochastic processes with independent increments, stationary process, and the ergodic theorem. 5. Brownian motion and diffusions.

CILO-1: Recognize the basic theories and concepts of stochastic processes, such as increments, stationarity and ergodicity. CILO-2: Apply Markov chains, Poisson process and Brownian motion methods to solve the real-world problems in various fields, including statistics, probability and finance. CILO-3: Utilize the knowledge of stochastic process to construct mathematical models to analyze and interpret experimental data.