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Some Boundary Problems for Processes Continuous from below with Independent Increments. Their Connection with the Distribution of w(t)

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Stochastic Processes in Queueing Theory

Part of the book series: Applications of Mathematics ((SMAP,volume 4))

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Abstract

We have already seen that the assumption that the governing process X(t) (see § 6) be one with independent increments immediately simplifies the form of Beneš’ equation and leads to compact formulae, such as, for example, the equality

$$P(w^c (t) \geqslant x) = - ah(x),$$

where h(x) is the renewal density of the process.

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© 1976 Springer-Verlag New York Inc.

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Borovkov, A.A. (1976). Some Boundary Problems for Processes Continuous from below with Independent Increments. Their Connection with the Distribution of w(t). In: Stochastic Processes in Queueing Theory. Applications of Mathematics, vol 4. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9866-3_3

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  • DOI: https://doi.org/10.1007/978-1-4612-9866-3_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9868-7

  • Online ISBN: 978-1-4612-9866-3

  • eBook Packages: Springer Book Archive

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