Stochastic Models

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Stochastic Models: Analysis and Applications

B. R. Bhat
Stochastic Models Analysis and Applications Book PDF

Author : B. R. Bhat
Publisher : New Age International
Page : 412 pages
File Size : 47,8 Mb
Release : 2004
Category : Mathematical statistics
ISBN : 8122412289

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Stochastic Models: Analysis and Applications by B. R. Bhat Pdf

The Book Presents A Systematic Exposition Of The Basic Theory And Applications Of Stochastic Models.Emphasising The Modelling Rather Than Mathematical Aspects Of Stochastic Processes, The Book Bridges The Gap Between The Theory And Applications Of These Processes.The Basic Building Blocks Of Model Construction Are Explained In A Step By Step Manner, Starting From The Simplest Model Of Random Walk And Proceeding Gradually To More Complicated Models. Several Examples Are Given Throughout The Text To Illustrate Important Analytical Properties As Well As To Provide Applications.The Book Also Includes A Detailed Chapter On Inference For Stochastic Processes. This Chapter Highlights Some Of The Recent Developments In The Subject And Explains Them Through Illustrative Examples.An Important Feature Of The Book Is The Complements And Problems Section At The End Of Each Chapter Which Presents (I) Additional Properties Of The Model, (Ii) Extensions Of The Model, And (Iii) Applications Of The Model To Different Areas.With All These Features, This Is An Invaluable Text For Post-Graduate Students Of Statistics, Mathematics And Operation Research.

An Introduction to Stochastic Modeling

Howard M. Taylor,Samuel Karlin
An Introduction to Stochastic Modeling Book PDF

Author : Howard M. Taylor,Samuel Karlin
Publisher : Academic Press
Page : 410 pages
File Size : 55,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269276

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An Introduction to Stochastic Modeling by Howard M. Taylor,Samuel Karlin Pdf

An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Stochastic Modeling

Nicolas Lanchier
Stochastic Modeling Book PDF

Author : Nicolas Lanchier
Publisher : Springer
Page : 303 pages
File Size : 51,8 Mb
Release : 2017-01-27
Category : Mathematics
ISBN : 9783319500386

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Stochastic Modeling by Nicolas Lanchier Pdf

Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler’s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright –Fisher model, Kingman’s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and MatlabTM.

Introduction to Stochastic Models

Roe Goodman
Introduction to Stochastic Models Book PDF

Author : Roe Goodman
Publisher : Courier Corporation
Page : 370 pages
File Size : 51,8 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9780486450377

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Introduction to Stochastic Models by Roe Goodman Pdf

Newly revised by the author, this undergraduate-level text introduces the mathematical theory of probability and stochastic processes. Using both computer simulations and mathematical models of random events, it comprises numerous applications to the physical and biological sciences, engineering, and computer science. Subjects include sample spaces, probabilities distributions and expectations of random variables, conditional expectations, Markov chains, and the Poisson process. Additional topics encompass continuous-time stochastic processes, birth and death processes, steady-state probabilities, general queuing systems, and renewal processes. Each section features worked examples, and exercises appear at the end of each chapter, with numerical solutions at the back of the book. Suggestions for further reading in stochastic processes, simulation, and various applications also appear at the end.

Stochastic Models of Systems

Vladimir S. Korolyuk,Vladimir V. Korolyuk
Stochastic Models of Systems Book PDF

Author : Vladimir S. Korolyuk,Vladimir V. Korolyuk
Publisher : Springer Science & Business Media
Page : 195 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146258

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Stochastic Models of Systems by Vladimir S. Korolyuk,Vladimir V. Korolyuk Pdf

In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematical models of real systems, through mathematical analysis of models based on simplification methods, to the interpretation of real stochastic systems. The stochastic models described here share the property that their evolutionary aspects develop under the influence of random factors. It has been assumed that the evolution takes place in a random medium, i.e. unilateral interaction between the system and the medium. As only Markovian models of random medium are considered in this book, the stochastic models described here are determined by two processes, a switching process describing the evolution of the systems and a switching process describing the changes of the random medium. Audience: This book will be of interest to postgraduate students and researchers whose work involves probability theory, stochastic processes, mathematical systems theory, ordinary differential equations, operator theory, or mathematical modelling and industrial mathematics.

Stochastic Models for Time Series

Paul Doukhan
Stochastic Models for Time Series Book PDF

Author : Paul Doukhan
Publisher : Springer
Page : 308 pages
File Size : 41,8 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9783319769387

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Stochastic Models for Time Series by Paul Doukhan Pdf

This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit theorems) are described under SRD; mixing and weak dependence are also reviewed. In closing, it describes moment techniques together with their relations to cumulant sums as well as an application to kernel type estimation.The appendix reviews basic probability theory facts and discusses useful laws stemming from the Gaussian laws as well as the basic principles of probability, and is completed by R-scripts used for the figures. Richly illustrated with examples and simulations, the book is recommended for advanced master courses for mathematicians just entering the field of time series, and statisticians who want more mathematical insights into the background of non-linear time series.

Stochastic Models with Power-Law Tails

Dariusz Buraczewski,Ewa Damek,Thomas Mikosch
Stochastic Models with Power Law Tails Book PDF

Author : Dariusz Buraczewski,Ewa Damek,Thomas Mikosch
Publisher : Springer
Page : 320 pages
File Size : 46,9 Mb
Release : 2016-07-04
Category : Mathematics
ISBN : 9783319296791

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Stochastic Models with Power-Law Tails by Dariusz Buraczewski,Ewa Damek,Thomas Mikosch Pdf

In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.

Optimization of Stochastic Models

Georg Ch. Pflug
Optimization of Stochastic Models Book PDF

Author : Georg Ch. Pflug
Publisher : Springer
Page : 382 pages
File Size : 45,9 Mb
Release : 1997-10-14
Category : Business & Economics
ISBN : 146128631X

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Optimization of Stochastic Models by Georg Ch. Pflug Pdf

Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research.

Stochastic Models in Biology

Narendra S. Goel,Nira Richter-Dyn
Stochastic Models in Biology Book PDF

Author : Narendra S. Goel,Nira Richter-Dyn
Publisher : Elsevier
Page : 282 pages
File Size : 40,7 Mb
Release : 2016-01-26
Category : Science
ISBN : 9781483278100

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Stochastic Models in Biology by Narendra S. Goel,Nira Richter-Dyn Pdf

Stochastic Models in Biology describes the usefulness of the theory of stochastic process in studying biological phenomena. The book describes analysis of biological systems and experiments though probabilistic models rather than deterministic methods. The text reviews the mathematical analyses for modeling different biological systems such as the random processes continuous in time and discrete in state space. The book also discusses population growth and extinction through Malthus' law and the work of MacArthur and Wilson. The text then explains the dynamics of a population of interacting species. The book also addresses population genetics under systematic evolutionary pressures known as deterministic equations and genetic changes in a finite population known as stochastic equations. The text then turns to stochastic modeling of biological systems at the molecular level, particularly the kinetics of biochemical reactions. The book also presents various useful equations such as the differential equation for generating functions for birth and death processes. The text can prove valuable for biochemists, cellular biologists, and researchers in the medical and chemical field who are tasked to perform data analysis.

Constructive Computation in Stochastic Models with Applications

Quan-Lin Li
Constructive Computation in Stochastic Models with Applications Book PDF

Author : Quan-Lin Li
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 40,6 Mb
Release : 2011-02-02
Category : Mathematics
ISBN : 9783642114922

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Constructive Computation in Stochastic Models with Applications by Quan-Lin Li Pdf

"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable. Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.

Stochastic Modeling

Barry L. Nelson
Stochastic Modeling Book PDF

Author : Barry L. Nelson
Publisher : Courier Corporation
Page : 338 pages
File Size : 49,5 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9780486139944

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Stochastic Modeling by Barry L. Nelson Pdf

Coherent introduction to techniques also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Includes formulation of models, analysis, and interpretation of results. 1995 edition.

Stochastic Models of Buying Behavior

William F. Massy,David Bruce Montgomery,Donald G. Morrison
Stochastic Models of Buying Behavior Book PDF

Author : William F. Massy,David Bruce Montgomery,Donald G. Morrison
Publisher : MIT Press (MA)
Page : 488 pages
File Size : 41,8 Mb
Release : 1970
Category : Business & Economics
ISBN : STANFORD:36105033952669

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Stochastic Models of Buying Behavior by William F. Massy,David Bruce Montgomery,Donald G. Morrison Pdf

Approaches to stochastic modeling; Estimating and testing stochastic models; Brand-choice models; Zero-order models; Two state markov models; Linear learning models for brand choice; A probability diffusion model; Application of the probability diffusion model; Purchase incidence models; Models for purchase timing and market penetration; A stochastic model for monitoring new product adoption; Parameter estimations and some emperical results for STEAM; Extension to STEAM.

Change-Point Analysis in Nonstationary Stochastic Models

Boris Brodsky
Change Point Analysis in Nonstationary Stochastic Models Book PDF

Author : Boris Brodsky
Publisher : CRC Press
Page : 366 pages
File Size : 54,6 Mb
Release : 2016-12-12
Category : Mathematics
ISBN : 9781498755979

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Change-Point Analysis in Nonstationary Stochastic Models by Boris Brodsky Pdf

This book covers the development of methods for detection and estimation of changes in complex systems. These systems are generally described by nonstationary stochastic models, which comprise both static and dynamic regimes, linear and nonlinear dynamics, and constant and time-variant structures of such systems. It covers both retrospective and sequential problems, particularly theoretical methods of optimal detection. Such methods are constructed and their characteristics are analyzed both theoretically and experimentally. Suitable for researchers working in change-point analysis and stochastic modelling, the book includes theoretical details combined with computer simulations and practical applications. Its rigorous approach will be appreciated by those looking to delve into the details of the methods, as well as those looking to apply them.

Stochastic Models, Statistics and Their Applications

Ansgar Steland,Ewaryst Rafajłowicz,Krzysztof Szajowski
Stochastic Models Statistics and Their Applications Book PDF

Author : Ansgar Steland,Ewaryst Rafajłowicz,Krzysztof Szajowski
Publisher : Springer
Page : 492 pages
File Size : 41,6 Mb
Release : 2015-02-04
Category : Mathematics
ISBN : 9783319138817

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Stochastic Models, Statistics and Their Applications by Ansgar Steland,Ewaryst Rafajłowicz,Krzysztof Szajowski Pdf

This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.

Stochastic Modelling and Control

M. H. A. Davis,Richard B. Vinter
Stochastic Modelling and Control Book PDF

Author : M. H. A. Davis,Richard B. Vinter
Publisher : Springer
Page : 416 pages
File Size : 50,6 Mb
Release : 1985
Category : Juvenile Nonfiction
ISBN : UCAL:B5008624

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Stochastic Modelling and Control by M. H. A. Davis,Richard B. Vinter Pdf

This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a 'black box' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.