To give information about basic concept of stochastic processes, concept of random processes, stationary, independences, first order, second order stationary process. To introduce Markov processes, counting processes, renewal processes, Brownian motion with specific examples.

Introduction to stochastic processes, Stationary, Independence, First order stationary process, Second order stationary process, Classifications of the stochastic processes, Purely random process, Markov process, Markov chain: discrete parameters, Transition probabilities, Recurrent and non-recurrent states and classes, Chapman-Kolmogorov equation, Mean absorption, first passage, and recurrence times, Limit theorems for occupation times, Limit theorems for transition probabilities, Markov chain: continuous parameters, Transition probabilities and intensities, Kolmogorov differential equations, Limit theorems for transition probabilities, Birth-death processes, Counting processes, Poisson processes, Non-homogeneous, compound Poisson processes Renewal processes, Examples of renewal processes, The renewal equation, The mean function of renewal processes, Brownian Motion, Introduction to Brownian Motion, Examples for Brownian Motion