Introduction to Stochastic Processes

Abstract

When considering technical, economic, ecological, or other problems, in several cases the quantities $\left \{ X_{t},\;t\in \mathcal {T}\right \}$ being examined can be regarded as a collection of random variables. This collection describes the changes (usually in time and in space) of considered quantities. If the set $\mathcal {T}$ is a subset of the set of real numbers, then the set $\left \{ t\in \mathcal {T}\right \}$ can be interpreted as time and we can say that the random quantities X_t vary in time. In this case the collection of random variables $\left \{ X_{t},\;t\in \mathcal {T} \right \}$ is called a stochastic process. In mathematical modeling of randomly varying quantities in time, one might rely on the highly developed theory of stochastic processes.