TY - JOUR
T1 - A basic result on the integral for birth-death Markov processes
AU - Hernández-Suárez, Carlos M.
AU - Castillo-Chavez, Carlos
N1 - Funding Information:
The authors wish to thank Charles E. McCulloch, Jorge Velasco-Hernández, Rich Durret and Sid Resnick for valuable comments. We also thank several anonymous referees for suggestions to improve this work. This research was partially supported by CONACYT grant 438100-5-I26932-M and by NSF funding to the Institute for Mathematics and its Applications at the University of Minnesota as well as by NSF and NSA funding to CCC, at the Mathematical and Theoretical Biology Institute at Cornell University.
PY - 1999
Y1 - 1999
N2 - In this paper a regenerative argument is used to derive an expression for the expectation of the integral under the stochastic path of a birth- death Markov process up to extinction time as well as for the expected time to extinction. Some applications to classical birth-death processes are given.
AB - In this paper a regenerative argument is used to derive an expression for the expectation of the integral under the stochastic path of a birth- death Markov process up to extinction time as well as for the expected time to extinction. Some applications to classical birth-death processes are given.
KW - Absorbing Markov processes
KW - Birth-death processes
KW - Integrals of Markov processes
KW - Queuing theory
UR - http://www.scopus.com/inward/record.url?scp=0032741459&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032741459&partnerID=8YFLogxK
U2 - 10.1016/S0025-5564(99)00034-6
DO - 10.1016/S0025-5564(99)00034-6
M3 - Article
C2 - 10546443
AN - SCOPUS:0032741459
SN - 0025-5564
VL - 161
SP - 95
EP - 104
JO - Mathematical Biosciences
JF - Mathematical Biosciences
IS - 1-2
ER -