Stochastic processes are mathematical models of random phenomena that
evolve according to prescribed dynamics. Processes commonly used in
applications are Markov chains in discrete and continuous time, renewal
and regenerative processes, Poisson processes, and Brownian motion. This
volume gives an in-depth description of the structure and basic
properties of these stochastic processes. A main focus is on equilibrium
distributions, strong laws of large numbers, and ordinary and functional
central limit theorems for cost and performance parameters. Although
these results differ for various processes, they have a common trait of
being limit theorems for processes with regenerative increments.
Extensive examples and exercises show how to formulate stochastic models
of systems as functions of a system's data and dynamics, and how to
represent and analyze cost and performance measures. Topics include
stochastic networks, spatial and space-time Poisson processes, queueing,
reversible processes, simulation, Brownian approximations, and varied
Markovian models.
The technical level of the volume is between that of introductory texts
that focus on highlights of applied stochastic processes, and advanced
texts that focus on theoretical aspects of processes.