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Stochastic Processes

Author: Richard F. Bass
Publisher: Cambridge University Press
ISBN: 113950147X
Size: 18.35 MB
Format: PDF
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This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black–Scholes formula for the pricing of derivatives in financial mathematics, the Kalman–Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.

Probability

Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 113949113X
Size: 69.84 MB
Format: PDF
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This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Probability Theory

Author: Daniel W. Stroock
Publisher: Cambridge University Press
ISBN: 1139494619
Size: 67.58 MB
Format: PDF, ePub
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This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given.

Probability Random Processes And Statistical Analysis

Author: Hisashi Kobayashi
Publisher: Cambridge University Press
ISBN: 1139502611
Size: 65.92 MB
Format: PDF
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Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.

Probability A Lively Introduction

Author: Henk Tijms
Publisher: Cambridge University Press
ISBN: 1108418740
Size: 78.31 MB
Format: PDF
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Comprehensive, yet concise, this textbook is the go-to guide to learn why probability is so important and its applications.

Convergence Of Stochastic Processes

Author: David Pollard
Publisher: David Pollard
ISBN: 0387909907
Size: 51.93 MB
Format: PDF, Kindle
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Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.

Random Graph Dynamics

Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 1139460889
Size: 10.61 MB
Format: PDF
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The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Continuous Martingales And Brownian Motion

Author: Daniel Revuz
Publisher: Springer Science & Business Media
ISBN: 3662064006
Size: 39.79 MB
Format: PDF, Docs
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"This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises." –BULLETIN OF THE L.M.S.

Brownian Motion

Author: René L. Schilling
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110307308
Size: 63.63 MB
Format: PDF, Docs
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Stochastic processes occur everywhere in sciences and engineering, and need to be understood by applied mathematicians, engineers and scientists alike. This is a first course introducing the reader gently to the subject. Brownian motions are a stochastic process, central to many applications and easy to treat.

Brownian Motion

Author: Peter Mörters
Publisher: Cambridge University Press
ISBN: 1139486578
Size: 18.93 MB
Format: PDF
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This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.