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Author : Hans R. Lerche
Publisher :
ISBN 13 : 9781461565703
Total Pages : 152 pages
Book Rating : 4.5/5 (657 download)
Download or read book Boundary Crossing of Brownian Motion written by Hans R. Lerche and published by . This book was released on 2014-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hans R. Lerche
Publisher : Springer Science & Business Media
ISBN 13 : 1461565693
Total Pages : 147 pages
Book Rating : 4.4/5 (615 download)
Download or read book Boundary Crossing of Brownian Motion written by Hans R. Lerche and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a research report about my work on sequential statistic~ during 1980 - 1984. Two themes are treated which are closely related to each other and to the law of the iterated logarithm:· I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries. In the first chapter I discuss the tangent approximation for Brownianmotion as a global approximation device. This is an extension of Strassen' s approach to t'he law of the iterated logarithm which connects results of fluctuation theory of Brownian motion with classical methods of sequential statistics. In the second chapter I make use of these connections and derive optimal properties of tests of power one and repeated significance tests for the simpiest model of sequential statistics, the Brownian motion with unknown drift. To both topics:there under1ies an asymptotic approach which is closely linked to large deviation theory: the stopping boundaries recede to infinity. This is a well-known approach in sequential stötistics which is extensively discussed in Siegmund's recent book ·Sequential Analysis". This approach also leads to some new insights about the law of the iterated logarithm (LIL). Although the LIL has been studied for nearly seventy years the belief is still common that it applies only for large sampIe sizes which can never be obser ved in practice.
Author : Thomas H. Scheike
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (912 download)
Download or read book Working paper written by Thomas H. Scheike and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Liqun Wang
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (314 download)
Download or read book Boundary Crossing Probability for Brownian Motion and General Boundaries written by Liqun Wang and published by . This book was released on 1994 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas H. Scheike
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (315 download)
Download or read book A Boundary Crossing Result for the Brownian Motion written by Thomas H. Scheike and published by . This book was released on 1990 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tung-Lung Wu (Jr.)
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.:/5 (855 download)
Download or read book Linear and Non-linear Boundary Crossing Probabilities for Brownian Motion and Related Processes written by Tung-Lung Wu (Jr.) and published by . This book was released on 2012 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.
Author : Moshe Pollak
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.:/5 (69 download)
Download or read book Asymptotic Problems Related to Boundary Crossing of One-dimensional Shifted Brownian Motion written by Moshe Pollak and published by . This book was released on 1973 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tung-Lung Jr Wu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)
Download or read book Linear and Non-linear Boundary Crossing Probabilities for Brownian Motion and Related Processes written by Tung-Lung Jr Wu and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.
Author : Ioannis Karatzas
Publisher : Springer
ISBN 13 : 1461209498
Total Pages : 490 pages
Book Rating : 4.4/5 (612 download)
Download or read book Brownian Motion and Stochastic Calculus written by Ioannis Karatzas and published by Springer. This book was released on 2014-03-27 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
Author : Zhiyong Jin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)
Download or read book A New Approach to the Computation of First Passage Time Distribution for Brownian Motion written by Zhiyong Jin and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis consists of two novel contributions to the computation of first passage time distribution for Brownian motion. First, we extend the known formula for boundary crossing probabilities for Brownian motion to the discontinuous piecewise linear boundary. Second, we derive explicit formula for the first passage time density of Brownian motion crossing piecewise linear boundary. Further, we demonstrate how to approximate the boundary crossing probabilities and density for general nonlinear boundaries. Moreover, we use Monte Carlo simulation method and develop algorithms for the numerical computation. This method allows one to assess the accuracy of the numerical approximation. Our approach can be further extended to compute two-sided boundary crossing probabilities.
Author : Peter Mörters
Publisher : Cambridge University Press
ISBN 13 : 1139486578
Total Pages : pages
Book Rating : 4.1/5 (394 download)
Download or read book Brownian Motion written by Peter Mörters and published by Cambridge University Press. This book was released on 2010-03-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Shelemyahu Zacks
Publisher : Springer
ISBN 13 : 331967059X
Total Pages : 141 pages
Book Rating : 4.3/5 (196 download)
Download or read book Sample Path Analysis and Distributions of Boundary Crossing Times written by Shelemyahu Zacks and published by Springer. This book was released on 2017-10-12 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is focused on the derivations of exact distributions of first boundary crossing times of Poisson processes, compound Poisson processes, and more general renewal processes. The content is limited to the distributions of first boundary crossing times and their applications to various stochastic models. This book provides the theory and techniques for exact computations of distributions and moments of level crossing times. In addition, these techniques could replace simulations in many cases, thus providing more insight about the phenomenona studied. This book takes a general approach for studying telegraph processes and is based on nearly thirty published papers by the author and collaborators over the past twenty five years. No prior knowledge of advanced probability is required, making the book widely available to students and researchers in applied probability, operations research, applied physics, and applied mathematics.
Author : Robert J. Adler
Publisher : IMS
ISBN 13 : 9780940600171
Total Pages : 198 pages
Book Rating : 4.6/5 (1 download)
Download or read book An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes written by Robert J. Adler and published by IMS. This book was released on 1990 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wolfgang Bischoff
Publisher :
ISBN 13 :
Total Pages : 7 pages
Book Rating : 4.:/5 (163 download)
Download or read book A Lower Bound for Boundary Crossing Probabilities of Brownian Bridge, Motion with Trend written by Wolfgang Bischoff and published by . This book was released on 2004 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Philip Nelson
Publisher : Macmillan Higher Education
ISBN 13 : 1319038948
Total Pages : 661 pages
Book Rating : 4.3/5 (19 download)
Download or read book Biological Physics written by Philip Nelson and published by Macmillan Higher Education. This book was released on 2013-12-16 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biological Physics focuses on new results in molecular motors, self-assembly, and single-molecule manipulation that have revolutionized the field in recent years, and integrates these topics with classical results. The text also provides foundational material for the emerging field of nanotechnology.
Author : Gregory F. Lawler
Publisher : American Mathematical Soc.
ISBN 13 : 0821848291
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)
Download or read book Random Walk and the Heat Equation written by Gregory F. Lawler and published by American Mathematical Soc.. This book was released on 2010-11-22 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.
Author : H. Kesten
Publisher : Springer Science & Business Media
ISBN 13 : 1461204593
Total Pages : 457 pages
Book Rating : 4.4/5 (612 download)
Download or read book Random Walks, Brownian Motion, and Interacting Particle Systems written by H. Kesten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. The last area was started by Frank as part of the general resurgence of treating problems of statistical mechanics with rigorous probabilistic tools.
