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First-Rare-Event Times for Semi-Markov Processes. Edition No. 1
VDM Publishing House, Feb 2009, Pages: 148
First-rare-event times often appear in probabilistic
research under such names as life time, ruin time,
stopping time, death time, catastrophic time,
extension time, epidemic time, record time, failure
time, killing time, passage time, hitting time,
absorption time, transition time, etc.
Notion of first-rare-event times is usually used to
describe the first occurrence of events which have
small probability of appearance. One of the
fundamental questions here is question of asymptotic
analysis of distributions of first-rare-event times
taking into account possible changes of model
characteristics. Semi-Markov processes are often
used for this kind of modeling.
This book is devoted to the analysis of conditions
of weak convergence of first-rare-event times for a
semi-Markov process with finite set of states in
both non-triangular array case and in the series of
schemes.
Book is oriented on professional researchers working
with asymptotic analysis of perturbed random
functionals defined on Markov chains and semi-Markov
processes.
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