Introduction to Stochastic Processes

László Lakatos, László Szeidl and Miklós Telek
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László Lakatos: Eötvös Loránd University
László Szeidl: Óbuda University
Miklós Telek: Budapest University of Technology and Economics

Chapter Chapter 2 in Introduction to Queueing Systems with Telecommunication Applications, 2013, pp 55-76 from Springer

Abstract: 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.

Keywords: Poisson Process; Random Point; Wiener Process; Independent Increment; Stationary Increment (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-5317-8_2

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