Limit theorems for the process of exceedances in large populations.
Rahimov, Ibrahim, Hasan, Husna (2000)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Rahimov, Ibrahim, Hasan, Husna (2000)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Jan M. Swart (2011)
Kybernetika
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It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling between a general birth-and-death process and a process whose birth rates are the negatives of...
Birkner, Matthias, Blath, Jochen, Capaldo, Marcella, Etheridge, Alison M., Möhle, Martin, Schweinsberg, Jason, Wakolbinger, Anton (2005)
Electronic Journal of Probability [electronic only]
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André Arnold (1988)
Banach Center Publications
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Jagers, Peter, Lagerås, Andreas Nordvall (2008)
Electronic Communications in Probability [electronic only]
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Andrzej Makagon (1999)
Studia Mathematica
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A one-to-one correspondence between locally square integrable periodically correlated (PC) processes and a certain class of infinite-dimensional stationary processes is obtained. The correspondence complements and clarifies Gladyshev's known result [3] describing the correlation function of a continuous periodically correlated process. In contrast to Gladyshev's paper, the procedure for explicit reconstruction of one process from the other is provided. A representation of a PC process...
Alexander Zeifman, Anna Korotysheva, Yacov Satin, Victor Korolev, Sergey Shorgin, Rostislav Razumchik (2015)
International Journal of Applied Mathematics and Computer Science
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Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, timedependent analysis...
Karpelevich, F.I., Suhov, Yu.M. (1997)
Journal of Applied Mathematics and Stochastic Analysis
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Kunze, M., Monteiro Marques, Manuel D.P. (1997)
Journal of Convex Analysis
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Lambert, Amaury (2007)
Electronic Journal of Probability [electronic only]
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Matthes, Klaus, Nawrotzki, Kurt, Siegmund-Schultze, Rainer (1997)
Serdica Mathematical Journal
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The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the...