Stochastic Modeling

Author : Nicolas Lanchier
Publisher : Springer
Page : 303 pages
File Size : 46,7 Mb
Release : 2017-01-27
Category : Mathematics
ISBN : 9783319500386

Get Book

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.

Author : Howard M. Taylor,Samuel Karlin
Publisher : Academic Press
Page : 410 pages
File Size : 52,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269276

Get Book

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.

Author : Barry L. Nelson
Publisher : Courier Corporation
Page : 338 pages
File Size : 42,9 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9780486139944

Get Book

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.

Author : Vladimir I. Rotar
Publisher : CRC Press
Page : 510 pages
File Size : 45,9 Mb
Release : 2012-08-25
Category : Mathematics
ISBN : 9781439872062

Get Book

Probability and Stochastic Modeling by Vladimir I. Rotar Pdf

A First Course in Probability with an Emphasis on Stochastic Modeling Probability and Stochastic Modeling not only covers all the topics found in a traditional introductory probability course, but also emphasizes stochastic modeling, including Markov chains, birth-death processes, and reliability models. Unlike most undergraduate-level probability texts, the book also focuses on increasingly important areas, such as martingales, classification of dependency structures, and risk evaluation. Numerous examples, exercises, and models using real-world data demonstrate the practical possibilities and restrictions of different approaches and help students grasp general concepts and theoretical results. The text is suitable for majors in mathematics and statistics as well as majors in computer science, economics, finance, and physics. The author offers two explicit options to teaching the material, which is reflected in "routes" designated by special "roadside" markers. The first route contains basic, self-contained material for a one-semester course. The second provides a more complete exposition for a two-semester course or self-study.

Author : Oliver Ibe
Publisher : Newnes
Page : 514 pages
File Size : 41,6 Mb
Release : 2013-05-22
Category : Mathematics
ISBN : 9780124078390

Get Book

Markov Processes for Stochastic Modeling by Oliver Ibe Pdf

Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. Presents both the theory and applications of the different aspects of Markov processes Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.

Author : Georg Ch. Pflug
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461314493

Get Book

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.

Author : Roe Goodman
Publisher : Courier Corporation
Page : 370 pages
File Size : 42,6 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9780486450377

Get Book

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,5 Mb
Release : 2010
Category : Actuarial science
ISBN : 098139681X

Get Book

Stochastic Modeling by Anonim Pdf

Author : Dariusz Buraczewski,Ewa Damek,Thomas Mikosch
Publisher : Springer
Page : 320 pages
File Size : 48,8 Mb
Release : 2016-07-04
Category : Mathematics
ISBN : 9783319296791

Get Book

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.

Author : Vladimir S. Korolyuk,Vladimir V. Korolyuk
Publisher : Springer Science & Business Media
Page : 195 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146258

Get Book

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.

Author : Ronald W. Wolff
Publisher : Pearson
Page : 580 pages
File Size : 45,7 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39015060607937

Get Book

Stochastic Modeling and the Theory of Queues by Ronald W. Wolff Pdf

An integrated and up-to-date treatment of applied stochastic processes and queueing theory, with an emphasis on time-averages and long-run behavior. Theory demonstrates practical effects, such as priorities, pooling of queues, and bottlenecks. Appropriate for senior/graduate courses in queueing theory in Operations Research, Computer Science, Statistics, or Industrial Engineering departments. (vs. Ross, Karlin, Kleinrock, Heyman)

Author : Peter Guttorp
Publisher : CRC Press
Page : 384 pages
File Size : 55,7 Mb
Release : 2018-03-29
Category : Mathematics
ISBN : 9781351413664

Get Book

Stochastic Modeling of Scientific Data by Peter Guttorp Pdf

Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.

Author : Paul Doukhan
Publisher : Springer
Page : 308 pages
File Size : 55,7 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9783319769387

Get Book

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 44,5 Mb
Release : 1988
Category : Electronic
ISBN : OCLC:471822265

Get Book

Stochastic Modelling and Analysis by Anonim Pdf

Author : Hossein Bonakdari,Mohammad Zeynoddin
Publisher : Elsevier
Page : 372 pages
File Size : 43,7 Mb
Release : 2022-04-13
Category : Business & Economics
ISBN : 9780323972758

Get Book

Stochastic Modeling by Hossein Bonakdari,Mohammad Zeynoddin Pdf

Stochastic Modeling: A Thorough Guide to Evaluate, Pre-Process, Model and Compare Time Series with MATLAB Software allows for new avenues in time series analysis and predictive modeling which summarize more than ten years of experience in the application of stochastic models in environmental problems. The book introduces a variety of different topics in time series in the modeling and prediction of complex environmental systems. Most importantly, all codes are user-friendly and readers will be able to use them for their cases. Users who may not be familiar with MATLAB software can also refer to the appendix. This book also guides the reader step-by-step to learn developed codes for time series modeling, provides required toolboxes, explains concepts, and applies different tools for different types of environmental time series problems. Provides video tutorials on the use of codes Includes a companion site with 3,000 lines of programming, 70 principal codes and 100 pseudo codes Highlights multiple methods to Illustrate each problem