This course learns fundamental aspects of discrete stochastic processes models and their applications. In particular, we studies the systems that evolve in time via random changes at discrete intervals, and understand their nature by analyzing them through insightful models. The discrete stochastic-process models are useful in many applications of operations research and finance, as well as engineering. We will cover…
- Counting processes and renewal processes
- Markov processes (finite and countable)
- Random walk and martingale processes
Renewal process can be considered a generalization of Poisson process. Given an event occurrence (i.e., renewal), we can ignore the past, and consider the process as a newly-starting process with the same statistical property.