Brownian Motion, Obstacles and Random Media

DOWNLOAD NOW »

Author: Alain-Sol Sznitman

Publisher: Springer Science & Business Media

ISBN: 3662112817

Category: Mathematics

Page: 357

View: 2735

This book provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. It also includes an overview of known results and connections with other areas of random media, taking a highly original and personal approach throughout.

Directed Polymers in Random Environments

École d'Été de Probabilités de Saint-Flour XLVI – 2016

DOWNLOAD NOW »

Author: Francis Comets

Publisher: Springer

ISBN: 3319504878

Category: Mathematics

Page: 199

View: 2845

Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.

Dynamics and Randomness II

DOWNLOAD NOW »

Author: Alejandro Maass,Servet Martínez,Jaime San Martín

Publisher: Springer Science & Business Media

ISBN: 9781402019906

Category: Mathematics

Page: 228

View: 680

This book contains the lectures given at the Second Conference on Dynamics and Randomness held at the Centro de Modelamiento Matemático of the Universidad de Chile, from December 9-13, 2003. This meeting brought together mathematicians, theoretical physicists, theoretical computer scientists, and graduate students interested in fields related to probability theory, ergodic theory, symbolic and topological dynamics. The courses were on: -Some Aspects of Random Fragmentations in Continuous Times; -Metastability of Ageing in Stochastic Dynamics; -Algebraic Systems of Generating Functions and Return Probabilities for Random Walks; -Recurrent Measures and Measure Rigidity; -Stochastic Particle Approximations for Two-Dimensional Navier Stokes Equations; and -Random and Universal Metric Spaces. The intended audience for this book is Ph.D. students on Probability and Ergodic Theory as well as researchers in these areas. The particular interest of this book is the broad areas of problems that it covers. We have chosen six main topics and asked six experts to give an introductory course on the subject touching the latest advances on each problem.

Random Operators

DOWNLOAD NOW »

Author: Michael Aizenman,Simone Warzel

Publisher: American Mathematical Soc.

ISBN: 1470419130

Category: Functional analysis -- Miscellaneous applications of functional analysis -- Applications in quantum physics

Page: 326

View: 2335

This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Annales de l'I.H.P.

Probabilités et statistiques

DOWNLOAD NOW »

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Probabilities

Page: N.A

View: 9115

Stochastic Analysis on Large Scale Interacting Systems

DOWNLOAD NOW »

Author: Tadahisa Funaki,Hirofumi Osada

Publisher: Mathematical Soc of Japan

ISBN: N.A

Category: Mathematics

Page: 395

View: 2337

This volume is a collection of 15 research and survey papers written by the speakers from two international conferences held in Japan, The 11th Mathematical Society of Japan International Research Institute's Stochastic Analysis on Large Scale Interacting Systems and Stochastic Analysis and Statistical Mechanics. Topics discussed in the volume cover the hydrodynamic limit, fluctuations, large deviations, spectral gap (Poincare inequality), logarithmic Sobolev inequality, Ornstein-Zernike asymptotics, random environments, determinantal expressions for systems including exclusion processes (stochastic lattice gas, Kawasaki dynamics), zero range processes, interacting Brownian particles, random walks, self-avoiding walks, Ginzburg-Landau model, interface models, Ising model, Widom-Rowlinson model, directed polymers, random matrices, Dyson's model, and more. The material is suitable for graduate students and researchers interested in probability theory, stochastic processes, and statistical mechanics.

Wahrscheinlichkeitstheorie und Stochastische Prozesse

DOWNLOAD NOW »

Author: Michael Mürmann

Publisher: Springer-Verlag

ISBN: 364238160X

Category: Mathematics

Page: 428

View: 6759

Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

Random Polymers

DOWNLOAD NOW »

Author: Frank Hollander

Publisher: Springer Science & Business Media

ISBN: 364200332X

Category: Mathematics

Page: 258

View: 9884

Polymer chains that interact with themselves and/or their environment display a range of physical and chemical phenomena. This text focuses on the mathematical description of some of these phenomena, offering a mathematical panorama of polymer chains.

Stochastic Integrals

An Introduction

DOWNLOAD NOW »

Author: Heinrich von Weizsäcker

Publisher: Springer-Verlag

ISBN: 3663139239

Category: Mathematics

Page: 332

View: 6527

Dirichlet Forms and Analysis on Wiener Space

DOWNLOAD NOW »

Author: Nicolas Bouleau,Francis Hirsch

Publisher: Walter de Gruyter

ISBN: 311085838X

Category: Mathematics

Page: 335

View: 7119

The subject of this book is analysis on Wiener space by means of Dirichlet forms and Malliavin calculus. There are already several literature on this topic, but this book has some different viewpoints. First the authors review the theory of Dirichlet forms, but they observe only functional analytic, potential theoretical and algebraic properties. They do not mention the relation with Markov processes or stochastic calculus as discussed in usual books (e.g. Fukushima’s book). Even on analytic properties, instead of mentioning the Beuring-Deny formula, they discuss “carré du champ” operators introduced by Meyer and Bakry very carefully. Although they discuss when this “carré du champ” operator exists in general situation, the conditions they gave are rather hard to verify, and so they verify them in the case of Ornstein-Uhlenbeck operator in Wiener space later. (It should be noticed that one can easily show the existence of “carré du champ” operator in this case by using Shigekawa’s H-derivative.) In the part on Malliavin calculus, the authors mainly discuss the absolute continuity of the probability law of Wiener functionals. The Dirichlet form corresponds to the first derivative only, and so it is not easy to consider higher order derivatives in this framework. This is the reason why they discuss only the first step of Malliavin calculus. On the other hand, they succeeded to deal with some delicate problems (the absolute continuity of the probability law of the solution to stochastic differential equations with Lipschitz continuous coefficients, the domain of stochastic integrals (Itô-Ramer-Skorokhod integrals), etc.). This book focuses on the abstract structure of Dirichlet forms and Malliavin calculus rather than their applications. However, the authors give a lot of exercises and references and they may help the reader to study other topics which are not discussed in this book. Zentralblatt Math, Reviewer: S.Kusuoka (Hongo)

Stochastik

Einführung in die Wahrscheinlichkeitstheorie und Statistik

DOWNLOAD NOW »

Author: Hans-Otto Georgii

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110359707

Category: Mathematics

Page: 448

View: 6639

Dieses Lehrbuch gibt eine Einführung in die "Mathematik des Zufalls", bestehend aus den beiden Teilbereichen Wahrscheinlichkeitstheorie und Statistik. Die stochastischen Konzepte, Modelle und Methoden werden durch typische Anwendungsbeispiele motiviert und anschließend systematisch entwickelt. Der dafür notwendige maßtheoretische Rahmen wird gleich zu Beginn auf elementarem Niveau bereitgestellt. Zahlreiche Übungsaufgaben, zum Teil mit Lösungsskizzen, illustrieren und ergänzen den Text. Zielgruppe sind Studierende der Mathematik ab dem dritten Semester, sowie Naturwissenschaftler und Informatiker mit Interesse an den mathematischen Grundlagen der Stochastik. Die 5. Auflage wurde nochmals bearbeitet und maßvoll ergänzt.

Elektronentheorie der Metalle

DOWNLOAD NOW »

Author: Hans Albrecht Bethe,Arnold Sommerfeld

Publisher: Springer

ISBN: N.A

Category: Electrons

Page: 290

View: 1555

JASA

DOWNLOAD NOW »

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Statistics

Page: N.A

View: 2253

Mathematik für Physiker und Ingenieure 1

Basiswissen für das Grundstudium - mit mehr als 1400 Aufgaben und Lösungen online

DOWNLOAD NOW »

Author: Klaus Weltner

Publisher: Springer-Verlag

ISBN: 3642300855

Category: Science

Page: 301

View: 9366

Das zweibändige Lehrwerk bietet eine gut verständliche Einführung in die mathematischen Grundlagen des Physik- und Ingenieurstudiums. Band 1 richtet sich an Studierende im ersten Semester (Bachelor). Die Lerninhalte werden begleitet von Erläuterungen zu den einzelnen Übungsschritten (Rückfragen, Aufgaben und Lösungen), welche auch online zur Verfügung stehen. Daher eignet sich das seit über 25 Jahren bewährte Lehrbuch hervorragend für das Selbststudium. Die 17. Auflage wurde überarbeitet und ergänzt.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance

DOWNLOAD NOW »

Author: Eckhard Platen,Nicola Bruti-Liberati

Publisher: Springer Science & Business Media

ISBN: 364213694X

Category: Mathematics

Page: 856

View: 2073

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.