Random Sums and Branching Stochastic Processes

Random Sums and Branching Stochastic Processes
Author: Ibrahim Rahimov
Publisher: Springer Science & Business Media
Total Pages: 207
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461242169

The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.

Adventures in Stochastic Processes

Adventures in Stochastic Processes
Author: Sidney I. Resnick
Publisher: Springer Science & Business Media
Total Pages: 640
Release: 2013-12-11
Genre: Mathematics
ISBN: 1461203872

Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed.

An Introduction to Stochastic Modeling

An Introduction to Stochastic Modeling
Author: Howard M. Taylor
Publisher: Academic Press
Total Pages: 410
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483269272

An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

An Introduction to Stochastic Modeling

An Introduction to Stochastic Modeling
Author: Howard M. Taylor
Publisher: Academic Press
Total Pages: 579
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483220443

An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Combinatorial Stochastic Processes

Combinatorial Stochastic Processes
Author: Jim Pitman
Publisher: Springer Science & Business Media
Total Pages: 257
Release: 2006-05-11
Genre: Mathematics
ISBN: 354030990X

The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

The Theory of Stochastic Processes II

The Theory of Stochastic Processes II
Author: I.I. Gikhman
Publisher: Springer Science & Business Media
Total Pages: 464
Release: 2004-03-22
Genre: Mathematics
ISBN: 9783540202851

From the Reviews: "To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing." --K.L. Chung, American Scientist, 1977