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Stochastic Processes

Author: Richard F. Bass
Publisher: Cambridge University Press
ISBN: 113950147X
Size: 15.27 MB
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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.

Convergence Of Stochastic Processes

Author: David Pollard
Publisher: David Pollard
ISBN: 0387909907
Size: 53.31 MB
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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: 44.48 MB
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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.

Probability And Stochastics

Author: Erhan Çınlar
Publisher: Springer Science & Business Media
ISBN: 9780387878591
Size: 13.12 MB
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This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author’s lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Cinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.

Theory Of Stochastic Processes

Author: Dmytro Gusak
Publisher: Springer Science & Business Media
ISBN: 9780387878621
Size: 20.49 MB
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Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.

Advances In Directional And Linear Statistics

Author: Martin T. Wells
Publisher: Springer Science & Business Media
ISBN: 9783790826289
Size: 71.22 MB
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The present volume consists of papers written by students, colleagues and collaborators of Sreenivasa Rao Jammalamadaka from various countries, and covers a variety of research topics which he enjoys and contributed immensely to.

Markov Chains

Author: J. R. Norris
Publisher: Cambridge University Press
ISBN: 9780521633963
Size: 59.39 MB
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In this rigorous account the author studies both discrete-time and continuous-time chains. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials, in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and a careful selection of exercises and examples drawn both from theory and practice. This is an ideal text for seminars on random processes or for those that are more oriented towards applications, for advanced undergraduates or graduate students with some background in basic probability theory.

Stochastic Processes 2nd Ed

Author: SHELDON M. ROSS
Publisher:
ISBN: 9788126517572
Size: 58.45 MB
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Market_Desc: · Statisticians· Engineers· Computer Scientists· Senior/Graduate Level Students· Professors of Stochastics Processes Special Features: · Focuses on the application of stochastic process with emphasis on queuing networks and reversibility. · Describes processes from a probabilistic instead of an analytical point of view. About The Book: The book provides a non measure theoretic introduction to stochastic processes, probabilistic intuition and insight in thinking about problems. This revised edition contains additional material on compound Poisson random variables including an identity which can be used to efficiently compute moments, Poisson approximations; and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs.

Quantum Stochastic Processes And Noncommutative Geometry

Author: Kalyan B. Sinha
Publisher: Cambridge University Press
ISBN: 1139461699
Size: 44.34 MB
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The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.

Gaussian Processes On Trees

Author: Anton Bovier
Publisher: Cambridge University Press
ISBN: 1107160499
Size: 62.26 MB
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Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.