Asymptotic expansion for the distribution of absorption time of a semi-Markov process

1979 ◽  
Vol 30 (3) ◽  
pp. 331-335 ◽  
Author(s):  
A. Tadzhiev
2020 ◽  
Vol 57 (4) ◽  
pp. 1045-1069
Author(s):  
Matija Vidmar

AbstractFor a spectrally negative self-similar Markov process on $[0,\infty)$ with an a.s. finite overall supremum, we provide, in tractable detail, a kind of conditional Wiener–Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of this absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existing results in the literature.


1993 ◽  
Vol 30 (3) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.


Biometrics ◽  
2008 ◽  
Vol 64 (4) ◽  
pp. 1301-1301
Author(s):  
Mei-Jie Zhang

1987 ◽  
Vol 24 (2) ◽  
pp. 203-224 ◽  
Author(s):  
David E. Fousler ◽  
Samuel Karlin

1974 ◽  
Vol 11 (01) ◽  
pp. 193-198 ◽  
Author(s):  
Edward P. C. Kao

This paper derives results for computing the first two moments of times in transient states and times to absorption in a transient semi-Markov process. An illustrative example is presented at the end.


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