Random Walk A Modern Introduction

Author: Gregory F. Lawler
Publisher: Cambridge University Press
ISBN: 1139488767
Format: PDF, Mobi
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Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.

Random Walks Brownian Motion and Interacting Particle Systems

Author: H. Kesten
Publisher: Springer Science & Business Media
ISBN: 1461204593
Format: PDF, ePub
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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.

Elements of the Random Walk

Author: Joseph Rudnick
Publisher: Cambridge University Press
ISBN: 9781139450140
Format: PDF, ePub, Mobi
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Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.

Random Walks in Biology

Author: Howard C. Berg
Publisher: Princeton University Press
ISBN: 9780691000640
Format: PDF
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This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.

Folgen Wechselkurse einem Random Walk

Author: Heiko Wößner
Publisher: GRIN Verlag
ISBN: 3638697533
Format: PDF, ePub, Docs
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Studienarbeit aus dem Jahr 2001 im Fachbereich VWL - Geldtheorie, Geldpolitik, Note: 1,0, Eberhard-Karls-Universitat Tubingen (VWL - Wirtschaftstheorie), Veranstaltung: Bestimmungsgrunde des Wechselkurses: Erklarungsversuche und Puzzles, Sprache: Deutsch, Anmerkungen: Prognosefahigkeit verschiedener Wechselkursvorhersagemodelle: u.a. Kaufkraftparitaten-, Zinsparitatentheorie und Overshooting., Abstract: In den letzten Jahren bzw. Jahrzehnten hat sich das Volumen im Devisenhandel weltweit dramatisch erhoht, da mit zunehmend international orientiertem Handel die Bedeutung auslandischer Markte fur die heimische Wirtschaft stark gestiegen ist. Nahezu alle Unternehmen produzieren heutzutage nicht mehr nur fur das Inland, sondern auch fur den auslandischen Absatzmarkt. Ausserdem sind oft auch einige Lieferanten in einem anderen Wahrungsraum beheimatet, so dass hier sehr schnell die Abhangigkeit der Firmen vom Wechselkurs erkennbar wird. Sowohl fur Banken, die an auslandische Unternehmen oder auch Regierungen Kredite vergeben, als auch fur Privatpersonen spielt das Verhaltnis der nationalen Wahrung zu anderen eine wichtige Rolle. Eine Kernaussage der Portfoliotheorie besagt, dass durch Diversifikation des investierten Vermogens Risiko verringert werden kann. Mittels einer regionalen Streuung ist es moglich, die Folgen eines Schocks fur ein einzelnes Land abzumildern. Werden Investitionen im Ausland getatigt, ist fur die Gesamtrendite jedoch auch die Entwicklung des Wechselkurses von entscheidender Bedeutung. Begeben Regierungen oder Unternehmen am Kapitalmarkt Anleihen, die in fremder Wahrung notieren, so sind sie naturlich ebenso von Veranderungen des Wahrungswertes betroffen. Dies stellt nur eine kurz Ubersicht uber einige Akteure dar, die taglich mit Wechselkursschwankungen konfrontiert sind. Ihnen allen ist das Interesse an der zukunftigen Entwicklung gemeinsam, so dass hier Bedarf an Prognosen fur kunftige Kurse vorhanden ist. Lasst sich aber diese Nachfrage ube

Random Walks Critical Phenomena and Triviality in Quantum Field Theory

Author: Roberto Fernandez
Publisher: Springer Science & Business Media
ISBN: 3662028662
Format: PDF, Kindle
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Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.