The objective here is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts in stochastic processes — Markov chains and stochastic analysis. The readers are lead directly to the core of the topics, and further details are collated in a section containing abundant exercises and more materials for further reading and studying.In the part on Markov chains, the core is the ergodicity. By using the minimal non-negative solution method, we deal with the recurrence and various ergodicity. This is done step by step, from...