Model Theory Of Stochastic Processes

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Model Theory Of Stochastic Processes

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Author : Sergio Fajardo
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-30

Model Theory Of Stochastic Processes written by Sergio Fajardo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-30 with Mathematics categories.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourteenth publication in the Lecture Notes in Logic series, Fajardo and Keisler present new research combining probability theory and mathematical logic. It is a general study of stochastic processes using ideas from model theory, a key central theme being the question, 'When are two stochastic processes alike?' The authors assume some background in nonstandard analysis, but prior knowledge of model theory and advanced logic is not necessary. This volume will appeal to mathematicians willing to explore new developments with an open mind.

Stochastic Processes General Theory

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Author : Malempati M. Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Stochastic Processes General Theory written by Malempati M. Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.

Probability Stochastic Processes And Queueing Theory

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Author : Randolph Nelson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Probability Stochastic Processes And Queueing Theory written by Randolph Nelson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

We will occasionally footnote a portion of text with a "**,, to indicate Notes on the that this portion can be initially bypassed. The reasons for bypassing a Text portion of the text include: the subject is a special topic that will not be referenced later, the material can be skipped on first reading, or the level of mathematics is higher than the rest of the text. In cases where a topic is self-contained, we opt to collect the material into an appendix that can be read by students at their leisure. The material in the text cannot be fully assimilated until one makes it Notes on "their own" by applying the material to specific problems. Self-discovery Problems is the best teacher and although they are no substitute for an inquiring mind, problems that explore the subject from different viewpoints can often help the student to think about the material in a uniquely per sonal way. With this in mind, we have made problems an integral part of this work and have attempted to make them interesting as well as informative.

Model Theory Of Stochastic Processes

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Author : Sergio Fajardo
language : en
Publisher: A K Peters/CRC Press
Release Date : 2002-01-01

Model Theory Of Stochastic Processes written by Sergio Fajardo and has been published by A K Peters/CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.

This book presents new research in probability theory using ideas from mathematical logic. It is a general study of stochastic processes on adapted probability spaces, employing the concept of similarity of stochastic processes based on the notion of adapted distribution. The authors use ideas from model theory and methods from nonstandard analysis. The construction of spaces with certain richness properties, defined by insights from model theory, becomes easy using nonstandard methods, but remains difficult or impossible without them.

Theory And Applications Of Stochastic Processes

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Author : Zeev Schuss
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-09

Theory And Applications Of Stochastic Processes written by Zeev Schuss and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-09 with Mathematics categories.

Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

Stochastic Processes

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Author : Pierre Del Moral
language : en
Publisher: CRC Press
Release Date : 2017-02-24

Stochastic Processes written by Pierre Del Moral and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-24 with Mathematics categories.

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

Adventures In Stochastic Processes

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Author : Sidney I. Resnick
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11

Adventures In Stochastic Processes written by Sidney I. Resnick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. In a lively and imaginative presentation, studded with examples, exercises, and applications, and supported by inclusion of computational procedures, the author has created a textbook that provides easy access to this fundamental topic for many students of applied sciences at many levels. With its carefully modularized discussion and crystal clear differentiation between rigorous proof and plausibility argument, it is accessible to beginners but flexible enough to serve as well those who come to the course with strong backgrounds. The prerequisite background for reading the book is a graduate level pre-measure theoretic probability course. No knowledge of measure theory is presumed and advanced notions of conditioning are scrupulously avoided until the later chapters of the book. The tools of applied probability---discrete spaces, Markov chains, renewal theory, point processes, branching processes, random walks, Brownian motion---are presented to the reader in illuminating discussion. Applications include such topics as queuing, storage, risk analysis, genetics, inventory, choice, economics, sociology, and other. Because of the conviction that analysts who build models should know how to build them for each class of process studied, the author has included such constructions.

Stochastic Models Information Theory And Lie Groups Volume 1

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Author : Gregory S. Chirikjian
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-02

Stochastic Models Information Theory And Lie Groups Volume 1 written by Gregory S. Chirikjian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.

This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

The Theory Of Stochastic Processes

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Author : Iosif I. Gikhman
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-22

The Theory Of Stochastic Processes written by Iosif I. Gikhman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-22 with Mathematics categories.

From the Reviews: "Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection." D.W. Stroock in Bulletin of the American Mathematical Society, 1980 "To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The set when completed will be an invaluable source of information and reference in this ever-expanding field" K.L. Chung in American Scientist, 1977 "..., the subject has grown enormously since 1953, and there will never be a true successor to Doob's book, but Gihman and Skorohod's three volumes will, I think, occupy a rather similar position as an invaluable tool of reference for all probability theorists. ... The dominant impression is of the authors' mastery of their material, and of their confident insight into its underlying structure. ..." J.F.C. Kingman in Bulletin of the London Mathematical Society, 1977

Introduction To Stochastic Processes

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Author : Mu-fa Chen
language : en
Publisher: World Scientific
Release Date : 2021-05-25

Introduction To Stochastic Processes written by Mu-fa Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-25 with Mathematics categories.

The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.