Basic Introduction

We are all aware that in applied statistics after we collect the empirical data, a theoretical probability distribution is fitted in order to extract more information from the data. If the fit is good (which depends on some tests), then the properties of the set of data can be approximated by that of the theoretical distribution. In a similar way, a real life process may have the characteristics of a stochastic process (what we mean by a stochastic process will be made clear in due course of time), and our aim is to understand the underlying theoretical stochastic processes which would fit the practical data to the maximum possible extent. Hence a good knowledge of the characteristics and behaviour of stochastic processes is required to understand many real life situations.

In general there are examples where probability models are suitable and very often a better way of representation of the probability model would be to consider a collection or family of random variables (r.v's) that are indexed by a parameter such as time or space. These models are what we define as stochastic process or random or chance process.