Stationary stochastic processes : theory and applications /: theory and applications. (2012)

• Record Type: Book
• Further Information: Note: Georg Lindgren.
• Other Names: Lindgren, Georg, 1940-
• Contents: Some Probability and Process Background; Sample space, sample function, and observables; Random variables and stochastic processes; Stationary processes and fields; Gaussian processes; Four historical landmarks; ; Sample Function Properties ; Quadratic mean properties; Sample function continuity; Derivatives, tangents, and other characteristics; Stochastic integration; An ergodic result; Exercises; ; Spectral Representations ; Complex-valued stochastic processes; Bochner’s theorem and the spectral distribution; Spectral representation of a stationary process; Gaussian processes; Stationary counting processes; Exercises; ; Linear Filters – General Properties ; Linear time invariant filters; Linear filters and differential equations; White noise in linear systems; Long range dependence, non-integrable spectra, and unstable systems; The ARMA-family; ; Linear Filters – Special Topics ; The Hilbert transform and the envelope; The sampling theorem; Karhunen-Loève expansion; ; Classical Ergodic Theory and Mixing ; The basic ergodic theorem in L 2; Stationarity and transformations; The ergodic theorem, transformation view; The ergodic theorem, process view; Ergodic Gaussian sequences and processes; Mixing and asymptotic independence; ; Vector Processes and Random Fields ; Spectral representation for vector processes; Some random field theory; Exercises; ; Level Crossings and Excursions ; Level crossings and Rice’s formula; Poisson character of high-level crossings; Marked crossings and biased sampling; The Slepian model; Crossing problems for vector processes and fields; ; A Some Probability Theory ; Events, probabilities, and random variables; The axioms of probability; Expectations; Convergence; Characteristic functions; Hilbert space and random variables; ; B Spectral Simulation of Random Processes ; The Fast Fourier Transform, FFT; Random phase and amplitude; Simulation scheme; Difficulties and details; Summary; ; C Commonly Used Spectra ; ; D Solutions and Hints To Selected Exercises ; Some probability and process background; Sample function properties; Spectral and other representations; Linear filters – general properties; Linear filters – special topics; Ergodic theory and mixing; Vector processes and random fields; Level crossings and excursions; Some probability theory; ; Bibliography ; Index
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2012
• Extent: 1 online resource, illustrations
• Subjects: 519.22; Stationary processes; Stochastic analysis; MATHEMATICS / Probability & Statistics / General; MATHEMATICS / Probability & Statistics / Bayesian Analysis
• Languages: English
• ISBNs: 9781466557802
• Related ISBNs: 146655780X
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.