Journal of the Royal Statistical Society Series D (The Statistician) · 1994 · 137 citations · 1 references
EngineeringMathematicsProbability TheoryStochastic ModelingStochastic ProcessesBrownian MotionContinuous-time Stochastic ProcessesMarkov ProcessesPoint ProcessesStationary ProcessesStochastic CalculusIndependent IncrementsMartingalesSample Path PropertiesStochastic Process Analysis
The book introduces continuous‑parameter stochastic processes to graduate students. It systematically presents modern concepts and methods of stochastic processes, emphasizing sample‑path analysis that engineers and scientists find useful. The text covers six principal classes of stochastic processes, additional chapters on point processes, Brownian motion, and L2 spaces, and provides numerous examples, applications, and over 200 exercises drawn from the author’s lecture courses.
This graduate-level textbook presents an introduction to the theory of continuous parameter stochastical processes. It is designed to provide a systematic account of the basic concepts and methods from a modern point of view. The author emphasizes the study of the sample paths of the processes - an approach which engineers and scientists will appreciate since simple paths are often what are observed in experiments. In addition to six principal classes of stochastic processes (independent increments, stationary, strictly stationary, second order processes, Markov processes and discrete parameter martingales) which are discussed in some detail, there are also separate chapters on point processes, Brownian motion processes, and L2 spaces. The book is based on many years of lecture courses given by the author. Numerous examples and applications are presented and over 200 exercises are included to illustrate and explain the concepts discussed in the text.
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