Books in Probability theory and stochastic processes

Stochastic Differential Equations and Diffusion Processes

2nd Edition
Volume 24
June 28, 2014
N. Ikeda + 1 more
English
eBook
9 7 8 1 4 8 3 2 9 6 1 5 9

Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.

Mathematical Methods of Reliability Theory

1st Edition
June 20, 2014
B. V. Gnedenko + 2 more
Z. W. Birnbaum + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 3 5 1 9

Mathematical Methods of Reliability Theory discusses fundamental concepts of probability theory, mathematical statistics, and an exposition of the relationships among the fundamental quantitative characteristics encountered in the theory. The book deals with the set-theoretic approach to reliability theory and the central concepts of set theory to the phenomena. It also presents methods of finding estimates for reliability parameters based on observations and methods of testing reliability hypotheses. Based on mathematical statistics, the book also explains formulation of some selected results. It presents a method that increases the reliability of manufactured articles—redundancy. An important part of product quality control is the standards of acceptance-sampling plans which require simplicity, wide content for flexibility, comprehensive characteristics, and variability. The book also tackles economical and rational methods of sampling inspections, highlighting the need for a correct evaluation of environmental conditions—the factors which predetermine the choice of the inspection method. The book then explains how to estimate the efficiency of the operation of the sampling plan after its selection. The book can be helpful for engineers, mathematicians, economists, or industrial managers, as well as for other professionals who work in the technological, political, research, structural, and physico-chemical areas.

Fundamentals of Applied Probability and Random Processes

2nd Edition
June 13, 2014
Oliver Ibe
English
Hardback
9 7 8 0 1 2 8 0 0 8 5 2 2
eBook
9 7 8 0 1 2 8 0 1 0 3 5 8

The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study.

Theory of Markov Processes

1st Edition
May 12, 2014
E. B. Dynkin
T. Köváry
English
eBook
9 7 8 1 4 8 3 2 2 6 1 0 1

Theory of Markov Processes provides information pertinent to the logical foundations of the theory of Markov random processes. This book discusses the properties of the trajectories of Markov processes and their infinitesimal operators. Organized into six chapters, this book begins with an overview of the necessary concepts and theorems from measure theory. This text then provides a general definition of Markov process and investigates the operations that make possible an inspection of the class of Markov processes corresponding to a given transition function. Other chapters consider the more complicated operation of generating a subprocess. This book discusses as well the construction of Markov processes with given transition functions. The final chapter deals with the conditions to be imposed on the transition function so that among the Markov processes corresponding to this function, there should be at least one. This book is a valuable resource for mathematicians, students, and research workers.

Stochastic Modelling of Social Processes

1st Edition
May 10, 2014
Andreas Diekmann + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 6 5 6 5

Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians.

Stochastic Analysis

1st Edition
May 10, 2014
Eddy Mayer-Wolf + 2 more
English
eBook
9 7 8 1 4 8 3 2 1 8 7 0 0

Stochastic Analysis: Liber Amicorum for Moshe Zakai focuses on stochastic differential equations, nonlinear filtering, two-parameter martingales, Wiener space analysis, and related topics. The selection first ponders on conformally invariant and reflection positive random fields in two dimensions; real time architectures for the Zakai equation and applications; and quadratic approximation by linear systems controlled from partial observations. Discussions focus on predicted miss, review of basic sequential detection problems, multigrid algorithms for the Zakai equation, invariant test functions and regularity, and reflection positivity. The text then takes a look at a model of stochastic differential equation in Hubert spaces applicable to Navier Stokes equation in dimension 2; wavelets as attractors of random dynamical systems; and Markov properties for certain random fields. The publication examines the anatomy of a low-noise jump filter, nonlinear filtering with small observation noise, and closed form characteristic functions for certain random variables related to Brownian motion. Topics include derivation of characteristic functions for the examples, proof of the theorem, sequential quadratic variation test, asymptotic optimal filters, mean decision time, and asymptotic optimal filters. The selection is a valuable reference for researchers interested in stochastic analysis.

Frontiers of Pattern Recognition

1st Edition
May 10, 2014
Satosi Watanabe
English
eBook
9 7 8 1 4 8 3 2 6 8 9 4 1

Frontiers of Pattern Recognition contains the proceedings of the International Conference on Frontiers of Pattern Recognition which took place on January 18-20, 1971, at the University of Hawaii, Honolulu. The compendium consists of 30 papers from authorities from eleven different countries, which describe the frontiers of pattern recognition as viewed from diverse viewpoints. Topics discussed include some techniques for recognizing structures in pictures, grammatical inference, syntactic pattern recognition and stochastic languages, and pattern cognition and the organization of information. Also covered are subjects on human face recognition, cluster analysis, and learning algorithms of pattern recognition in non-stationary conditions. Computer scientists, mathematicians, statisticians, linguists, and psychologists will find the book informative.

Applied Stochastic Processes

1st Edition
May 9, 2014
G. Adomian
English
eBook
9 7 8 1 4 8 3 2 5 9 0 8 6

Applied Stochastic Processes is a collection of papers dealing with stochastic processes, stochastic equations, and their applications in many fields of science. One paper discusses stochastic systems involving randomness in the system itself that can be a large dynamical multi-input, multi-output system. Examples of a large system are the national economy of a major country or when an acoustic wave is propagating as in the atmosphere, ocean, or sea. Another paper proves that only the average properties of the molecules of biology can be measured with precision in the test tube; and disputes a "simplistic" model of the cell as defined by a miniature Laplaces' universe. The paper notes that the way existing cells are constructed implies that quantum mechanical principles lead to certain questions (about simple experiments) having only statistical answers. Another paper addresses the detection of distributed, fluctuating targets in a reverberation limited, randomly time, and space varying transmission media. This approach is done by using the concepts of "random Green's functions" and the "stochastic Green's function." The collection will prove useful for cellular researchers, mathematicians, physicist, engineers, and academicians in the field of applied mathematics, statistics, and chemistry.

An Introduction to Measure-Theoretic Probability

2nd Edition
March 19, 2014
George G. Roussas
English
Hardback
9 7 8 0 1 2 8 0 0 0 4 2 7
eBook
9 7 8 0 1 2 8 0 0 2 9 0 2

An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching the basics of measure theoretic probability. This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics, probability and other related areas should be equipped with. This edition requires no prior knowledge of measure theory, covers all its topics in great detail, and includes one chapter on the basics of ergodic theory and one chapter on two cases of statistical estimation. Topics range from the basic properties of a measure to modes of convergence of a sequence of random variables and their relationships; the integral of a random variable and its basic properties; standard convergence theorems; standard moment and probability inequalities; the Hahn-Jordan Decomposition Theorem; the Lebesgue Decomposition T; conditional expectation and conditional probability; theory of characteristic functions; sequences of independent random variables; and ergodic theory. There is a considerable bend toward the way probability is actually used in statistical research, finance, and other academic and nonacademic applied pursuits. Extensive exercises and practical examples are included, and all proofs are presented in full detail. Complete and detailed solutions to all exercises are available to the instructors on the book companion site. This text will be a valuable resource for graduate students primarily in statistics, mathematics, electrical and computer engineering or other information sciences, as well as for those in mathematical economics/finance in the departments of economics.

Effective Dynamics of Stochastic Partial Differential Equations

1st Edition
February 27, 2014
Jinqiao Duan + 1 more
English
Hardback
9 7 8 0 1 2 8 0 0 8 8 2 9
eBook
9 7 8 0 1 2 8 0 1 2 6 9 7

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension.

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