A simple interpretation of two stochastic processes subject to an independent death process.
Gani, Joseph, Swift, Randall J. (2009)
Applied Mathematics E-Notes [electronic only]
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Gani, Joseph, Swift, Randall J. (2009)
Applied Mathematics E-Notes [electronic only]
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Miloslav Jiřina (1958)
Czechoslovak Mathematical Journal
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Birkner, Matthias, Blath, Jochen (2009)
Electronic Journal of Probability [electronic only]
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Karpelevich, F.I., Suhov, Yu.M. (1997)
Journal of Applied Mathematics and Stochastic Analysis
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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...
Petr Lachout (1992)
Commentationes Mathematicae Universitatis Carolinae
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Discussion on the limits in distribution of processes under joint rescaling of space and time is presented in this paper. The results due to Lamperti (1962), Weissman (1975), Hudson Mason (1982) and Laha Rohatgi (1982) are improved here.
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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