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On a class of spatial renewal processes: Renewal processes synchronization probabilities

Statistics & Probability Letters, 2020
Let \(X_{i}=(X_{i}^{(1)},\dots,X_{i}^{(d)}),i=1,2,\dots\) denote i.i.d. nonnegative random vectors and let \(S_{n}=(S_{n}^{(1)},\dots,S_{n}^{(d)})\) denote the sequence of partial sums. In renewal theory one studies the process \(N(B)=\) the number of \(n\) so that \(S_{n}\in B\), and the renewal measure \(M_{N}(B)=EN(B)\).
Karamzadeh, M.   +2 more
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Fuzzy random renewal process and renewal reward process

Fuzzy Optimization and Decision Making, 2007
Stochastic renewal theory is a well developed part of the theory of stochastic processes. The first author and \textit{B. Liu} [Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 11, No. 5, 573--586 (2003; Zbl 1076.60516)] have discussed renewal problems where interarrival times and rewards are fuzzy variables.
Zhao, Ruiqing   +2 more
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Compound Renewal Processes

2022
Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and ...
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Nested renewal processes

Advances in Applied Probability, 1980
A class of stochastic processes useful in the investigation of the deterioration and replacement of equipment, as well as in the study of group arrival/batch service queues, storage systems, epidemics and computer software, is introduced. These so-called nested renewal processes consist of ordinary and cumulative renewal processes sequentially nested ...
Ansell, J., Bendell, A., Humble, S.
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RENEWAL REWARD PROCESSES

1969
Abstract : The paper considers a process in which rewards are being earned and for which there exist time points at which the process begins anew--that is, that there exists an embedded renewal process. An expression for the asymptotic mean reward earned during any time interval is then obtained.
Sheldon M. Ross, Mark Brown
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