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基本説明
Intended for students taking a second a course in stochastic processes, this textbook presents an overview of theory with applications in engineering and science.
Full Description
Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field's widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes.
Features
Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields
Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability
Motivates mathematical theory from a statistical model-building viewpoint
Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes
Provides more than 100 exercises with hints to solutions and selected full solutions
This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.
Contents
Some Probability and Process Background. Sample Function Properties. Spectral Representations. Linear Filters - General Properties. Linear Filters - Special Topics. Classical Ergodic Theory and Mixing. Vector Processes and Random Fields. Level Crossings and Excursions.
