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 Xt 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.
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References
Apostol, T.: Calculus I. Wiley, Hoboken (1967)
Campbell, N.: Discontinuities in light emission. In: Proceedings of the Cambridge Philosophical Society, vol. 15, pp. 310–328. Cambridge University, Cambridge (1910)
Karlin, S., Taylor, H.M.: A First Course in Stochastic Processes. Academic, New York (1975)
Kingman, J.F.C.: Poisson Processes. Clerendon, Oxford (1993)
Serfozo, R.: Basics of Applied Stochastic Processes. Springer, Berlin (2009)
Snyder, D.L.: Random Point Processes. Wiley, New York (1975)
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Lakatos, L., Szeidl, L., Telek, M. (2019). Introduction to Stochastic Processes. In: Introduction to Queueing Systems with Telecommunication Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-15142-3_2
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DOI: https://doi.org/10.1007/978-3-030-15142-3_2
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