This course is an introduction to the theory of stochastic processes. Informally, astochastic process is a random quantity that evolves over time, like a gambler’s netfortune and the price fluctuations of a stock on any stock exchange, for instance.The main aims of this course are: 1) to provide a thorough but straightforward account of basic probability theory; 2) to introduce basic ideas and tools of the theoryof stochastic processes; and 3) to discuss in depth through many examples important stochastic processes, including Markov Chains (both in discrete and continuous time), Poisson processes, Brownian motion and Martingales. The course will alsocover other important but less routine topics, like Markov decision processes andsome elements of queueing theory.
