TY - JOUR
T1 - First passage times of birth-death processes and simple random walks
AU - Masuda, Yasushi
PY - 1988
Y1 - 1988
N2 - It is known that the first passage time of a birth death process from n to n+1 has a completely monotone density, however, the discrete analogue for a simple random walk does not hold. In this paper, first passage times of simple random walks from n to n+1 and from 0 to n are characterized. This discrepancy between the first passage time structures of birth-death process and simple random walks is also analyzed.
AB - It is known that the first passage time of a birth death process from n to n+1 has a completely monotone density, however, the discrete analogue for a simple random walk does not hold. In this paper, first passage times of simple random walks from n to n+1 and from 0 to n are characterized. This discrepancy between the first passage time structures of birth-death process and simple random walks is also analyzed.
KW - birth death processes
KW - complete monotonicity
KW - generalized phase type distributions
KW - simple random walks
KW - uniformization
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U2 - 10.1016/0304-4149(88)90027-0
DO - 10.1016/0304-4149(88)90027-0
M3 - Article
AN - SCOPUS:38249030081
VL - 29
SP - 51
EP - 63
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 1
ER -