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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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Renewal Process

2023
Sivaprasad Madhira, Shailaja Deshmukh
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7. Renewal of Process

2016
After proceedings commence by issuing a claim form or other originating process, they must be brought to the attention of the defendants or respondents by service. Generally, originating process remains valid for the purpose of service for a period of four months. Service of proceedings marks a watershed in the litigation process.
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Discrete Renewal Processes

IEEE Transactions on Reliability, 1971
Discrete renewal processes until recently have not been applied to the mathematical modeling of physical processes. Analyses of such renewal processes have proceeded on the basis of generating functions but the results are often too complicated to be of use.
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