This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.
This revised edition contains additional material on compound Poisson random variables including an identity which can be used to efficiently compute moments; a new chapter on Poisson approximations; and coverage of the mean time spent in ...
where ax denotes the common mean of the random variables X (t), —00 < t < 00. Since rx(s, t) depends only on the difference between s and t, (4) rx(s, t) = rx(0, t — s), —00 < s,t < 00. The function rx(t), —00 < t < 00, defined by rX(t) ...
The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.
J.M. Harrison . Brownian Motion and Stochastic Flow Systems , Wiley , New York ( 1985 ) . R.A. Howard . Dynamic Programming and Markov Processes , M.I.T. Press , Cambridge , MA ( 1960 ) . M. Iosifescu and P. Tautu . Stochastic ...
This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes.
This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes.
The random walk; Markov chains; Markov processes with discrete states in continuous time; Markov processes in continuous time with continuous state space; Non-markovian processes; Stationary processes: time domain; Stationary processes: ...
Random sequences; Processes in continuous time; Miscellaneous statistical applications; Limiting stochastic operations; Stationary processes; Prediction and communication theory; The statistical analysis of stochastic processes; Correlation ...
This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.
This book is devoted to the theory and applications of nonparametic functional estimation and prediction.