Random Processes By Example
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Random Processes By Example
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Author : Mikhail Lifshits
language : en
Publisher: World Scientific
Release Date : 2014-03-07
Random Processes By Example written by Mikhail Lifshits and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-07 with Mathematics categories.
This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a “teletraffic model”. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Lévy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations.The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes.
Random Processes For Engineers
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Author : Bruce Hajek
language : en
Publisher: Cambridge University Press
Release Date : 2015-03-12
Random Processes For Engineers written by Bruce Hajek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Computers categories.
An engaging introduction to the critical tools needed to design and evaluate engineering systems operating in uncertain environments.
Random Processes By Example
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Author : Mikhail Lifshits
language : en
Publisher: World Scientific
Release Date : 2014
Random Processes By Example written by Mikhail Lifshits and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes. Next, it illustrates general concepts by handling a transparent but rich example of a OC teletraffic modelOCO. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable L(r)vy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations. The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes. Sample Chapter(s). Chapter 1: Preliminaries (367 KB). Contents: Preliminaries: Random Variables: A Summary; From Poisson to Stable Variables; Limit Theorems for Sums and Domains of Attraction; Random Vectors; Random Processes: Random Processes: Main Classes; Examples of Gaussian Random Processes; Random Measures and Stochastic Integrals; Limit Theorems for Poisson Integrals; L(r)vy Processes; Spectral Representations; Convergence of Random Processes; Teletraffic Models: A Model of Service System; Limit Theorems for the Workload; Micropulse Model; Spacial Extensions. Readership: Graduate students and researchers in probability & statist
Probability Random Processes And Ergodic Properties
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Author : Robert M. Gray
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Probability Random Processes And Ergodic Properties written by Robert M. Gray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
This book has been written for several reasons, not all of which are academic. This material was for many years the first half of a book in progress on information and ergodic theory. The intent was and is to provide a reasonably self-contained advanced treatment of measure theory, prob ability theory, and the theory of discrete time random processes with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inc1ined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability . Much of the material is familiar stuff for mathematicians, but many of the topics and results have not previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and dis courage them from the second part. Hence I finally followed the suggestion to separate the material and split the project in two. The original justification for the present manuscript was the pragmatic one that it would be a shame to waste all the effort thus far expended. A more idealistic motivation was that the presentation bad merit as filling a unique, albeit smaIl, hole in the literature.
Introduction To Probability Statistics And Random Processes
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Author : Hossein Pishro-Nik
language : en
Publisher:
Release Date : 2014-08-15
Introduction To Probability Statistics And Random Processes written by Hossein Pishro-Nik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with Probabilities categories.
The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.
Applications Of Random Process Excursion Analysis
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Author : Irina S. Brainina
language : en
Publisher: Elsevier
Release Date : 2013-07-19
Applications Of Random Process Excursion Analysis written by Irina S. Brainina and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Technology & Engineering categories.
This book addresses one of the key problems in signal processing, the problem of identifying statistical properties of excursions in a random process in order to simplify the theoretical analysis and make it suitable for engineering applications. Precise and approximate formulas are explained, which are relatively simple and can be used for engineering applications such as the design of devices which can overcome the high initial uncertainty of the self-training period. The information presented in the monograph can be used to implement adaptive signal processing devices capable of detecting or recognizing the wanted signals (with a priori unknown statistical properties) against the background noise. The applications presented can be used in a wide range of fields including medicine, radiolocation, telecommunications, surface quality control (flaw detection), image recognition, thermal noise analysis for the design of semiconductors, and calculation of excessive load in mechanics.
Introduction To Random Signals And Noise
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Author : Wim C. Van Etten
language : en
Publisher: John Wiley & Sons
Release Date : 2006-02-03
Introduction To Random Signals And Noise written by Wim C. Van Etten and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-03 with Science categories.
Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals. Key features: Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains. Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver. Examines optimal filtering methods and their consequences. Presents a detailed discussion of the topic of Poisson processes and shot noise. An excellent resource for professional engineers developing communication systems, semiconductor devices, and audio and video equipment, this book is also ideal for senior undergraduate and graduate students in Electronic and Electrical Engineering.
Gaussian Random Processes
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Author : I.A. Ibragimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Gaussian Random Processes written by I.A. Ibragimov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.
Probability And Random Processes
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Author : A. Bruce Clarke
language : en
Publisher: John Wiley & Sons
Release Date : 1991-01-16
Probability And Random Processes written by A. Bruce Clarke and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-16 with Technology & Engineering categories.
A comprehensive textbook for undergraduate courses in introductory probability. Offers a case study approach, with examples from engineering and the social and life sciences. Updated second edition includes advanced material on stochastic processes. Suitable for junior and senior level courses in industrial engineering, mathematics, business, biology, and social science departments.
Stochastic Processes And Applications
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Author : Grigorios A. Pavliotis
language : en
Publisher: Springer
Release Date : 2014-11-19
Stochastic Processes And Applications written by Grigorios A. Pavliotis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.