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| Author | : Sheldon M. Ross |
| Publisher | : Courier Corporation |
| Total Pages | : 226 |
| Release | : 2013-04-15 |
| Genre | : Mathematics |
| ISBN | : 0486318648 |
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 | : Ingram Olkin |
| Publisher | : World Scientific |
| Total Pages | : 732 |
| Release | : 2019-09-03 |
| Genre | : Mathematics |
| ISBN | : 9813202068 |
Written by renowned experts in the field, this reissue of a textbook has as its unifying theme the role that probability models have had, and continue to have, in scientific and practical applications. It includes many examples, with actual data, of real-world use of probability models, while expositing the mathematical theory of probability at an introductory calculus-based level. Detailed descriptions of the properties and applications of probability models that have successfully modeled real phenomena are given, as well as an explanation of methods for testing goodness of fit of these models. Readers will receive a firm foundation in techniques for deriving distributions of various summaries of data that will prepare them for subsequent studies of statistics, as well as a solid grounding in concepts such as that of conditional probability that will prepare them for more advanced courses in stochastic processes.
| Author | : Sheldon Mark Ross |
| Publisher | : |
| Total Pages | : 198 |
| Release | : 1970 |
| Genre | : Mathematical optimization |
| ISBN | : 9780317262544 |
| Author | : Sheldon M. Ross |
| Publisher | : Academic Press |
| Total Pages | : 801 |
| Release | : 2006-12-11 |
| Genre | : Mathematics |
| ISBN | : 0123756871 |
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 | : Sheldon M. Ross |
| Publisher | : Academic Press |
| Total Pages | : 801 |
| Release | : 2006-11-17 |
| Genre | : Mathematics |
| ISBN | : 0080920179 |
Ross's classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It provides an introduction to elementary probability theory and stochastic processes, and shows 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. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. A new section (3.7) on COMPOUND RANDOM VARIABLES, that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions. A new section (4.11) on HIDDDEN MARKOV CHAINS, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states. Simplified Approach for Analyzing Nonhomogeneous Poisson processes Additional results on queues relating to the (a) conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system; (b) inspection paradox for M/M/1 queues (c) M/G/1 queue with server breakdown Many new examples and exercises.
| Author | : Sheldon M. Ross |
| Publisher | : |
| Total Pages | : 198 |
| Release | : 1970 |
| Genre | : Probabilities |
| ISBN | : |
| Author | : Do Le Minh |
| Publisher | : Brooks/Cole |
| Total Pages | : 360 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : |
Intended for a course in Probability Models at the undergraduate or graduate level, this book is designed for those who will actually use probability and is designed to fit diverse audiences (business students, applied engineering students, and biology students). The course focuses on applications of probability through the presentation of models rather than theory alone. In this practical and interesting book, author Do Le (Paul) Minh provides accessible coverage for a course in probability models. Minh motivates the material with interesting application problems relating to medicine, business, and engineering, many of which are based on real studies and applications. Throughout the book, he thoughtfully integrates the use of computers and spreadsheets to solve problems.
| Author | : M.H.A. Davis |
| Publisher | : CRC Press |
| Total Pages | : 316 |
| Release | : 1993-08-01 |
| Genre | : Mathematics |
| ISBN | : 9780412314100 |
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 | : J. George Shanthikumar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461551919 |
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability in solving problems in modern society.
