Models of Random Processes

Book excerpt: Devising and investigating random processes that describe mathematical models of phenomena is a major aspect of probability theory applications. Stochastic methods have penetrated into an unimaginably wide scope of problems encountered by researchers who need stochastic methods to solve problems and further their studies. This handbook supplies the knowledge you need on the modern theory of random processes. Packed with methods, Models of Random Processes: A Handbook for Mathematicians and Engineers presents definitions and properties on such widespread processes as Poisson, Markov, semi-Markov, Gaussian, and branching processes, and on special processes such as cluster, self-exiting, double stochastic Poisson, Gauss-Poisson, and extremal processes occurring in a variety of different practical problems. The handbook is based on an axiomatic definition of probability space, with strict definitions and constructions of random processes. Emphasis is placed on the constructive definition of each class of random processes, so that a process is explicitly defined by a sequence of independent random variables and can easily be implemented into the modelling. Models of Random Processes: A Handbook for Mathematicians and Engineers will be useful to researchers, engineers, postgraduate students and teachers in the fields of mathematics, physics, engineering, operations research, system analysis, econometrics, and many others.