## An Introduction to Stochastic Modeling

**Author**: Howard M. Taylor,Samuel Karlin

**Publisher:**Academic Press

**ISBN:**1483220443

**Category:**Mathematics

**Page:**578

**View:**3858

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An Introduction to Stochastic Modeling, Revised Edition 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.

## An Introduction to Stochastic Modeling, Student Solutions Manual (e-only)

**Author**: Mark Pinsky,Samuel Karlin

**Publisher:**Academic Press

**ISBN:**9780123852267

**Category:**Mathematics

**Page:**510

**View:**8993

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An Introduction to Stochastic Modeling, Student Solutions Manual (e-only)

## An Introduction to Differential Equations

*Stochastic Modeling, Methods and Analysis(Volume 2)*

**Author**: Anil G Ladde,G S Ladde

**Publisher:**World Scientific Publishing Company

**ISBN:**9814397393

**Category:**Mathematics

**Page:**636

**View:**4794

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Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)

## An Introduction to Continuous-Time Stochastic Processes

*Theory, Models, and Applications to Finance, Biology, and Medicine*

**Author**: Vincenzo Capasso,David Bakstein

**Publisher:**Birkhäuser

**ISBN:**1493927574

**Category:**Mathematics

**Page:**482

**View:**2592

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This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: Markov processes Stochastic differential equations Arbitrage-free markets and financial derivatives Insurance risk Population dynamics, and epidemics Agent-based models New to the Third Edition: Infinitely divisible distributions Random measures Levy processes Fractional Brownian motion Ergodic theory Karhunen-Loeve expansion Additional applications Additional exercises Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Edition will be of interest to a broad audience of students, pure and applied mathematicians, and researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduate courses, as well as European Masters courses (according to the two-year-long second cycle of the “Bologna Scheme”), the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. From reviews of previous editions: "The book is ... an account of fundamental concepts as they appear in relevant modern applications and literature. ... The book addresses three main groups: first, mathematicians working in a different field; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications." -Zentralblatt MATH

## Stochastic Modeling

*Analysis and Simulation*

**Author**: Barry L. Nelson

**Publisher:**Courier Corporation

**ISBN:**0486139948

**Category:**Mathematics

**Page:**336

**View:**4209

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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.

## An Introduction to Probability and Stochastic Processes

**Author**: James L. Melsa,Andrew P. Sage

**Publisher:**Courier Corporation

**ISBN:**0486490998

**Category:**Mathematics

**Page:**403

**View:**8660

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Detailed coverage of probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.

## An Introduction to Stochastic Filtering Theory

**Author**: Jie Xiong

**Publisher:**Oxford University Press on Demand

**ISBN:**0199219702

**Category:**Business & Economics

**Page:**270

**View:**1249

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As a topic, Stochastic Filtering Theory has progressed rapidly in recent years. For example, the (branching) particle system representation of the optimal filter has been extensively studied to seek more effective numerical approximations of the optimal filter. The stability of the filter with 'incorrect' initial state, as well as the long-term behavior of the optimal filter, has attracted the attention of many researchers, and there are some recent excitingresults in singular filtering models. In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering the key recent advances. The text is written in a clear style suitable for graduates in mathematics and engineering with a backgroundin basic probability.

## An Introduction to Stochastic Orders

**Author**: Felix Belzunce,Carolina Martinez Riquelme,Julio Mulero

**Publisher:**Academic Press

**ISBN:**0128038268

**Category:**Mathematics

**Page:**174

**View:**1817

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An Introduction to Stochastic Orders discusses this powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics. The book provides a general background on this topic for students and researchers who want to use it as a tool for their research. In addition, users will find detailed proofs of the main results and applications to several probabilistic models of interest in several fields, and discussions of fundamental properties of several stochastic orders, in the univariate and multivariate cases, along with applications to probabilistic models. Introduces stochastic orders and its notation Discusses different orders of univariate stochastic orders Explains multivariate stochastic orders and their convex, likelihood ratio, and dispersive orders

## An Introduction to Stochastic Dynamics

**Author**: Jinqiao Duan

**Publisher:**Cambridge University Press

**ISBN:**1107075394

**Category:**Mathematics

**Page:**307

**View:**5026

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An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.

## Introduction to Matrix Analytic Methods in Stochastic Modeling

**Author**: G. Latouche,V. Ramaswami

**Publisher:**SIAM

**ISBN:**0898714257

**Category:**Mathematics

**Page:**334

**View:**4671

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Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.

## An Introduction to Stochastic Processes in Physics

**Author**: Don S. Lemons,Paul Langevin

**Publisher:**JHU Press

**ISBN:**9780801868672

**Category:**Mathematics

**Page:**110

**View:**4823

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"Students will love this book. It tells them without fuss how to do simple and useful numerical calculations, with just enough background to understand what they are doing... a refreshingly brief and unconvoluted work." -- American Journal of Physics

## Introduction to Stochastic Processes

**Author**: Erhan Cinlar

**Publisher:**Courier Corporation

**ISBN:**0486276325

**Category:**Mathematics

**Page:**416

**View:**7076

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Clear presentation employs methods that recognize computer-related aspects of theory. Topics include expectations and independence, Bernoulli processes and sums of independent random variables, Markov chains, renewal theory, more. 1975 edition.

## Introduction to Stochastic Integration

**Author**: K.L. Chung,R.J. Williams

**Publisher:**Springer Science & Business Media

**ISBN:**1461495873

**Category:**Mathematics

**Page:**276

**View:**7609

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A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then It’s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman–Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed. New to the second edition are a discussion of the Cameron–Martin–Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. —Journal of the American Statistical Association An attractive text...written in [a] lean and precise style...eminently readable. Especially pleasant are the care and attention devoted to details... A very fine book. —Mathematical Reviews

## Introduction to Stochastic Models

**Author**: Marius Iosifescu,Nikolaos Limnios,Gheorghe Oprisan

**Publisher:**John Wiley & Sons

**ISBN:**1118623525

**Category:**Mathematics

**Page:**320

**View:**1645

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This book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and social sciences. It covers Markov and semi-Markov models, as well as their particular cases: Poisson, renewal processes, branching processes, Ehrenfest models, genetic models, optimal stopping, reliability, reservoir theory, storage models, and queuing systems. Given this comprehensive treatment of the subject, students and researchers in applied sciences, as well as anyone looking for an introduction to stochastic models, will find this title of invaluable use.

## Introduction to Probability Models

**Author**: Sheldon M. Ross

**Publisher:**Elsevier

**ISBN:**1483276589

**Category:**Mathematics

**Page:**568

**View:**5669

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Introduction to Probability Models, Fifth Edition focuses on different probability models of natural phenomena. This edition includes additional material in Chapters 5 and 10, such as examples relating to analyzing algorithms, minimizing highway encounters, collecting coupons, and tracking the AIDS virus. The arbitrage theorem and its relationship to the duality theorem of linear program are also covered, as well as how the arbitrage theorem leads to the Black-Scholes option pricing formula. Other topics include the Bernoulli random variable, Chapman-Kolmogorov equations, and properties of the exponential distribution. The continuous-time Markov chains, single-server exponential queueing system, variations on Brownian motion; and variance reduction by conditioning are also elaborated. This book is a good reference for students and researchers conducting work on probability models.

## An Introduction to Stochastic Differential Equations

**Author**: Lawrence C. Evans

**Publisher:**American Mathematical Soc.

**ISBN:**1470410540

**Category:**Mathematics

**Page:**151

**View:**1002

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These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

## An Introduction to Probabilistic Modeling

**Author**: Pierre Bremaud

**Publisher:**Springer Science & Business Media

**ISBN:**1461210461

**Category:**Mathematics

**Page:**208

**View:**1711

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Introduction to the basic concepts of probability theory: independence, expectation, convergence in law and almost-sure convergence. Short expositions of more advanced topics such as Markov Chains, Stochastic Processes, Bayesian Decision Theory and Information Theory.

## An Introduction to Mathematical Modeling

**Author**: Edward A. Bender

**Publisher:**Courier Corporation

**ISBN:**0486137120

**Category:**Mathematics

**Page:**272

**View:**3437

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Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

## An Introduction to Stochastic Processes

**Author**: Edward P. C. Kao

**Publisher:**Cengage Learning

**ISBN:**9780534255183

**Category:**Mathematics

**Page:**438

**View:**8344

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Intended for a calculus-based course in stochastic processes at the graduate or advanced undergraduate level, this text offers a modern, applied perspective. Instead of the standard formal and mathematically rigorous approach usual for texts for this course, Edward Kao emphasizes the development of operational skills and analysis through a variety of well-chosen examples.

## Introduction to Modeling and Analysis of Stochastic Systems

**Author**: V. G. Kulkarni

**Publisher:**Springer

**ISBN:**9781441917720

**Category:**Mathematics

**Page:**313

**View:**9834

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This book provides a self-contained review of all the relevant topics in probability theory. A software package called MAXIM, which runs on MATLAB, is made available for downloading. Vidyadhar G. Kulkarni is Professor of Operations Research at the University of North Carolina at Chapel Hill.