NDLI: Exit problems for the difference of a compound Poisson process and a compound renewal process

Content Provider	Springer Nature Link
Author	Kadankova, Tetyana Kadankov, Victor
Copyright Year	2008
Abstract	In this paper we solve a two-sided exit problem for a difference of a compound Poisson process and a compound renewal process. More specifically, we determine the Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the value of a linear component at this time instant. The results obtained are applied to solve the two-sided exit problem for a particular class of stochastic processes, i.e. the difference of the compound Poisson process and the renewal process whose jumps are exponentially distributed. The advantage is that these results are in a closed form, in terms of resolvent sequences of the process.We determine the Laplace transforms of the busy period of the systems M$^{ ϰ }$\|G$^{ δ }$\|1\|B, G$^{ δ }$\|M$^{ ϰ }$\|1\|B in case when δ∼exp (λ). Additionally, we prove the weak convergence of the two-boundary characteristics of the process to the corresponding functionals of the standard Wiener process.
Ending Page	296
Page Count	26
Starting Page	271
File Format	PDF
ISSN	02570130
e-ISSN	15729443
Journal	Queueing Systems
Issue Number	3-4
Volume Number	59
Language	English
Publisher	Springer US
Publisher Date	2008-09-10
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Value of the overshoot Difference of compound renewal processes Resolvent Systems Theory, Control Applications of Markov renewal processes (reliability, queueing networks, etc.) Operations Research/Decision Theory Production/Logistics Probability Theory and Stochastic Processes Stopping times; optimal stopping problems; gambling theory The first exit time Computer Communication Networks
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Management Science and Operations Research Computational Theory and Mathematics Computer Science Applications

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