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Author: Sheldon M. Ross
Publisher: Courier Corporation
ISBN: 0486318648
Category : Mathematics
Languages : en
Pages : 226
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Book Description
Concise advanced-level introduction to stochastic processes that arise in applied probability. Poisson process, renewal theory, Markov chains, Brownian motion, much more. Problems. References. Bibliography. 1970 edition.
Author: Sheldon M. Ross
Publisher: Courier Corporation
ISBN: 0486318648
Category : Mathematics
Languages : en
Pages : 226
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Book Description
Concise advanced-level introduction to stochastic processes that arise in applied probability. Poisson process, renewal theory, Markov chains, Brownian motion, much more. Problems. References. Bibliography. 1970 edition.
Author: M.H.A. Davis
Publisher: CRC Press
ISBN: 9780412314100
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This book presents a radically new approach to problems of evaluating and optimizing the performance of continuous-time stochastic systems. This approach is based on the use of a family of Markov processes called Piecewise-Deterministic Processes (PDPs) as a general class of stochastic system models. A PDP is a Markov process that follows deterministic trajectories between random jumps, the latter occurring either spontaneously, in a Poisson-like fashion, or when the process hits the boundary of its state space. This formulation includes an enormous variety of applied problems in engineering, operations research, management science and economics as special cases; examples include queueing systems, stochastic scheduling, inventory control, resource allocation problems, optimal planning of production or exploitation of renewable or non-renewable resources, insurance analysis, fault detection in process systems, and tracking of maneuvering targets, among many others. The first part of the book shows how these applications lead to the PDP as a system model, and the main properties of PDPs are derived. There is particular emphasis on the so-called extended generator of the process, which gives a general method for calculating expectations and distributions of system performance functions. The second half of the book is devoted to control theory for PDPs, with a view to controlling PDP models for optimal performance: characterizations are obtained of optimal strategies both for continuously-acting controllers and for control by intervention (impulse control). Throughout the book, modern methods of stochastic analysis are used, but all the necessary theory is developed from scratch and presented in a self-contained way. The book will be useful to engineers and scientists in the application areas as well as to mathematicians interested in applications of stochastic analysis.
Author: Sheldon M. Ross
Publisher: Academic Press
ISBN: 0123756871
Category : Mathematics
Languages : en
Pages : 801
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Book Description
Introduction to Probability Models, Tenth Edition, provides an introduction to elementary probability theory and stochastic processes. There are two approaches to the study of probability theory. One is heuristic and nonrigorous, and attempts to develop in students an intuitive feel for the subject that enables him or her to think probabilistically. The other approach attempts a rigorous development of probability by using the tools of measure theory. The first approach is employed in this text. The book begins by introducing basic concepts of probability theory, such as the random variable, conditional probability, and conditional expectation. This is followed by discussions of stochastic processes, including Markov chains and Poison processes. The remaining chapters cover queuing, reliability theory, Brownian motion, and simulation. Many examples are worked out throughout the text, along with exercises to be solved by students. This book will be particularly useful to those interested in learning how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. Ideally, this text would be used in a one-year course in probability models, or a one-semester course in introductory probability theory or a course in elementary stochastic processes. New to this Edition: - 65% new chapter material including coverage of finite capacity queues, insurance risk models and Markov chains - Contains compulsory material for new Exam 3 of the Society of Actuaries containing several sections in the new exams - Updated data, and a list of commonly used notations and equations, a robust ancillary package, including a ISM, SSM, and test bank - Includes SPSS PASW Modeler and SAS JMP software packages which are widely used in the field Hallmark features: - Superior writing style - Excellent exercises and examples covering the wide breadth of coverage of probability topics - Real-world applications in engineering, science, business and economics
Author: John Haigh
Publisher: Springer Science & Business Media
ISBN: 1447101693
Category : Mathematics
Languages : en
Pages : 263
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Book Description
Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability via dice and cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus, and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions.
Author: Urmila Diwekar
Publisher: Springer Science & Business Media
ISBN: 1475737459
Category : Mathematics
Languages : en
Pages : 342
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Book Description
This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without introducing excessive theoretical detail. This second edition includes additional topics, including global optimization and a real-world case study using important concepts from each chapter. Introduction to Applied Optimization is intended for advanced undergraduate and graduate students and will benefit scientists from diverse areas, including engineers.
Author: Sheldon M. Ross
Publisher: Academic Press
ISBN: 1483269094
Category : Mathematics
Languages : en
Pages : 179
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Book Description
Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented. The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.
Author: William P. Fox
Publisher: CRC Press
ISBN: 1000196925
Category : Mathematics
Languages : en
Pages : 417
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Book Description
Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB®, and MapleTM to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.
Author: Alexander Shapiro
Publisher: SIAM
ISBN: 1611976596
Category : Mathematics
Languages : en
Pages : 542
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Book Description
An accessible and rigorous presentation of contemporary models and ideas of stochastic programming, this book focuses on optimization problems involving uncertain parameters for which stochastic models are available. Since these problems occur in vast, diverse areas of science and engineering, there is much interest in rigorous ways of formulating, analyzing, and solving them. This substantially revised edition presents a modern theory of stochastic programming, including expanded and detailed coverage of sample complexity, risk measures, and distributionally robust optimization. It adds two new chapters that provide readers with a solid understanding of emerging topics; updates Chapter 6 to now include a detailed discussion of the interchangeability principle for risk measures; and presents new material on formulation and numerical approaches to solving periodical multistage stochastic programs. Lectures on Stochastic Programming: Modeling and Theory, Third Edition is written for researchers and graduate students working on theory and applications of optimization, with the hope that it will encourage them to apply stochastic programming models and undertake further studies of this fascinating and rapidly developing area.
Author: G. Dzemyda
Publisher: Springer Science & Business Media
ISBN: 1402004842
Category : Computers
Languages : en
Pages : 238
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Book Description
This book is dedicated to the 70th birthday of Professor J. Mockus, whose scientific interests include theory and applications of global and discrete optimization, and stochastic programming. The papers for the book were selected because they relate to these topics and also satisfy the criterion of theoretical soundness combined with practical applicability. In addition, the methods for statistical analysis of extremal problems are covered. Although statistical approach to global and discrete optimization is emphasized, applications to optimal design and to mathematical finance are also presented. The results of some subjects (e.g., statistical models based on one-dimensional global optimization) are summarized and the prospects for new developments are justified. Audience: Practitioners, graduate students in mathematics, statistics, computer science and engineering.
Author: Narayanaswamy Balakrishnan
Publisher: John Wiley & Sons
ISBN: 1118548558
Category : Mathematics
Languages : en
Pages : 548
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Book Description
INTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: Includes classroom-tested problems and solutions to probability exercises Highlights real-world exercises designed to make clear the concepts presented Uses Mathematica software to illustrate the text’s computer exercises Features applications representing worldwide situations and processes Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.
