Mathematics and Statistics - Probability and Statistics
A collection of random variables which is index by some mathematical set is referred to as a stochastic process. Index set is the set used to index these random variables. Each of these random variables takes its value from state space. The state space can be formed by integers, real line, etc. Because of its random nature, a stochastic process has multiple possible outcomes. A single outcome of such processes is known as sample function or realization. Stochastic processes can be further classified into Markov processes, Gaussian processes, random walks, martingales, branching processes and renewal processes. These processes find application in many fields such as ecology, signal processing, image processing, physics, biology, cryptology and financial markets. This book includes some of the vital pieces of work being conducted across the world, on various topics related to stochastic processes. It aims to shed light on some of the unexplored aspects of stochastic processes and the recent researches in this field. As this field is emerging at a rapid pace, the contents of this book will help the readers understand the modern concepts and applications of the subject.