Introduction to Stochastic Processes

László Lakatos, László Szeidl and Miklós Telek
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László Lakatos: Eotvos Lorant University
László Szeidl: Obuda University
Miklós Telek: Technical University of Budapest

Chapter Chapter 2 in Introduction to Queueing Systems with Telecommunication Applications, 2019, pp 63-91 from Springer

Abstract: Abstract When considering technical, economic, ecological, or other problems, in several cases the quantities X t , t ∈ T $$\left \{ X_{t},\;t\in \mathcal {T}\right \} $$ 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 T $$\mathcal {T}$$ is a subset of the set of real numbers, then the set t ∈ T $$\left \{ t\in \mathcal {T}\right \} $$ can be interpreted as time and we can say that the random quantities Xt vary in time. In this case the collection of random variables X t , t ∈ T $$\left \{ X_{t},\;t\in \mathcal {T} \right \} $$ is called a stochastic process. Stochastic process In mathematical modeling of randomly varying quantities in time, one might rely on the highly developed theory of stochastic processes.

Date: 2019
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DOI: 10.1007/978-3-030-15142-3_2

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