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Functional Analysis For Probability And Stochastic Processes

Author: Adam Bobrowski
Publisher: Cambridge University Press
ISBN: 9781139443883
Size: 55.59 MB
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This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

Theory Of Probability And Random Processes

Author: Leonid Koralov
Publisher: Springer Science & Business Media
ISBN: 3540688293
Size: 70.79 MB
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A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion.

Stochastic Partial Differential Equations

Author: Helge Holden
Publisher: Springer Science & Business Media
ISBN: 0387894888
Size: 31.11 MB
Format: PDF, Mobi
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The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise. Applications of the theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.

Real Analysis And Probability

Author: R. M. Dudley
Publisher: Cambridge University Press
ISBN: 9780521007542
Size: 31.42 MB
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This classic graduate textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The comprehensive historical notes have been further amplified for this new edition, and a number of new exercises have been added, together with hints for solution.

Probability And Stochastic Processes

Author: Roy D. Yates
Publisher: John Wiley & Sons
ISBN: 1118324560
Size: 37.91 MB
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This text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first seven chapters contain the core material that is essential to any introductory course. In one-semester undergraduate courses, instructors can select material from the remaining chapters to meet their individual goals. Graduate courses can cover all chapters in one semester.

Probability Theory Random Processes And Mathematical Statistics

Author: Y. Rozanov
Publisher: Springer Science & Business Media
ISBN: 9401104492
Size: 28.72 MB
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Probability Theory, Theory of Random Processes and Mathematical Statistics are important areas of modern mathematics and its applications. They develop rigorous models for a proper treatment for various 'random' phenomena which we encounter in the real world. They provide us with numerous tools for an analysis, prediction and, ultimately, control of random phenomena. Statistics itself helps with choice of a proper mathematical model (e.g., by estimation of unknown parameters) on the basis of statistical data collected by observations. This volume is intended to be a concise textbook for a graduate level course, with carefully selected topics representing the most important areas of modern Probability, Random Processes and Statistics. The first part (Ch. 1-3) can serve as a self-contained, elementary introduction to Probability, Random Processes and Statistics. It contains a number of relatively sim ple and typical examples of random phenomena which allow a natural introduction of general structures and methods. Only knowledge of elements of real/complex analysis, linear algebra and ordinary differential equations is required here. The second part (Ch. 4-6) provides a foundation of Stochastic Analysis, gives information on basic models of random processes and tools to study them. Here a familiarity with elements of functional analysis is necessary. Our intention to make this course fast-moving made it necessary to present important material in a form of examples.

Multiparameter Processes

Author: Davar Khoshnevisan
Publisher: Springer Science & Business Media
ISBN: 0387216316
Size: 14.54 MB
Format: PDF, Mobi
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Self-contained presentation: from elementary material to state-of-the-art research; Much of the theory in book-form for the first time; Connections are made between probability and other areas of mathematics, engineering and mathematical physics

Probability Theory And Stochastic Processes With Applications Second Edition

Author: Oliver Knill
Publisher: World Scientific Publishing Company
ISBN: 9789813109490
Size: 45.96 MB
Format: PDF, Docs
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This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.

Applied Probability And Stochastic Processes

Author: Michel K. Ochi
Publisher: Wiley-Interscience
Size: 67.42 MB
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This introduction to modern concepts of applied stochastic processes is written for a broad range of applications in diverse areas of engineering and the physical sciences (unlike other books, which are written primarily for communications or electrical engineering). Emphasis is on clarifying the basic principles supporting current prediction techniques. The first eight chapters present the probability theory relevant to analysis of stochastic processes. The following nine chapters discuss principles, advanced techniques (including the procedures of spectral analysis and the development of the probability density function) and applications. Also features material found in the recent literature such as higher-order spectral analysis, the joint probability distribution of amplitudes and periods and non-Gaussian random processes. Includes numerous illustrative examples.

Elementary Probability Theory With Stochastic Processes

Author: K. L. Chung
Publisher: Springer Science & Business Media
ISBN: 1475751141
Size: 31.51 MB
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In the past half-century the theory of probability has grown from a minor isolated theme into a broad and intensive discipline interacting with many other branches of mathematics. At the same time it is playing a central role in the mathematization of various applied sciences such as statistics, opera tions research, biology, economics and psychology-to name a few to which the prefix "mathematical" has so far been firmly attached. The coming-of-age of probability has been reflected in the change of contents of textbooks on the subject. In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution. This period ended with the appearance of Feller's classic treatise (see [Feller l]t) in 1950, from the manuscript of which I gave my first substantial course in probability. With the passage of time probability theory and its applications have won a place in the college curriculum as a mathematical discipline essential to many fields of study. The elements of the theory are now given at different levels, sometimes even before calculus. The present textbook is intended for a course at about the sophomore level. It presupposes no prior acquaintance with the subject and the first three chapters can be read largely without the benefit of calculus.