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Compound Renewal Processes (Hardcover)
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Compound Renewal Processes (Hardcover)
Series: Encyclopedia of Mathematics and its Applications
Expected to ship within 12 - 17 working days
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Compound renewal processes (CRPs) are among the most ubiquitous
models arising in applications of probability. At the same time,
they are a natural generalization of random walks, the most
well-studied classical objects in probability theory. This
monograph, written for researchers and graduate students, presents
the general asymptotic theory and generalizes many well-known
results concerning random walks. The book contains the key limit
theorems for CRPs, functional limit theorems, integro-local limit
theorems, large and moderately large deviation principles for CRPs
in the state space and in the space of trajectories, including
large deviation principles in boundary crossing problems for CRPs,
with an explicit form of the rate functionals, and an extension of
the invariance principle for CRPs to the domain of moderately large
and small deviations. Applications establish the key limit laws for
Markov additive processes, including limit theorems in the domains
of normal and large deviations.
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