Basics Of Applied Stochastic Processes (probability And Its Applications)
by Richard Serfozo /
2012 / English / PDF
2.6 MB Download
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.
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.
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.