0357433 20240903170622.520110307235959.9 000288625300001 14 s. WWW cav_un_epca*02971630023-5954471 (2011)1-14Ústav teorie informace a automatizace AV ČR, v. v. i. Intertwining of Markov processes birth and death process averaged Markov process first passage time coupling eigenvalues cav_un_auth*0217893 Swart Jan M. Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2011/SI/swart-intertwining of birth-and-death processes.pdf 205.8 KB GA201/09/1931 GA ČR cav_un_auth*0254026 CEZ:AV0Z10750506 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 the eigenvalues, ordered from high to low, and whose death rates are zero, in such a way that the latter process is always ahead of the former, and both arrive at the same time at the given level. In this note, we extend their methods by constructing a third process, whose birth rates are the negatives of the eigenvalues ordered from low to high and whose death rates are zero, which always lags behind the original process and also arrives at the same time. 2011 BA 4 O 4o 20231122134458.4 http://hdl.handle.net/11104/0195710 COMPUTERSCIENCECYBERNETICS 0.473 0.033 9.5 0.0016 0.277 403 61 21 0.307 20.45 0.61 Q2 23.915 17.500 Q4 Q3 2011 Soubory v repozitáři: 0357433.pdf 000288625300001 WOS 205.8 KB cav_un_epca*0297163 Kybernetika 0023-5954 Roč. 47 č. 1 2011 1 14 Ústav teorie informace a automatizace AV ČR, v. v. i.