## Brownian Motion, Obstacles and Random Media

**Author**: Alain-Sol Sznitman

**Publisher:**Springer Science & Business Media

**ISBN:**3662112817

**Category:**Mathematics

**Page:**357

**View:**4050

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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.

## Dynamics and Randomness II

**Author**: Alejandro Maass,Servet Martínez,Jaime San Martín

**Publisher:**Springer Science & Business Media

**ISBN:**9781402019906

**Category:**Mathematics

**Page:**228

**View:**3975

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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.

## Directed Polymers in Random Environments

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

**Author**: Francis Comets

**Publisher:**Springer

**ISBN:**3319504878

**Category:**Mathematics

**Page:**199

**View:**4436

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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.

## Random Operators

**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:**2502

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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.

## Mathematical Reviews

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**9153

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## Stochastic Analysis on Large Scale Interacting Systems

**Author**: Tadahisa Funaki,Hirofumi Osada

**Publisher:**Mathematical Soc of Japan

**ISBN:**N.A

**Category:**Mathematics

**Page:**395

**View:**5719

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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.

## Annales de l'I.H.P.

*Probabilités et statistiques*

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Probabilities

**Page:**N.A

**View:**7911

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## The number of sites visited by a random walk on an infinite graph

**Author**: Lee Randolph Gibson (1976-)

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**178

**View:**1974

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## American journal of mathematics

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**9756

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## Плиска; Бŭльгарски Математически Студии

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**2248

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## Abstracts of Papers Presented to the American Mathematical Society

**Author**: American Mathematical Society

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**2326

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## Random Polymers

**Author**: Frank Hollander

**Publisher:**Springer Science & Business Media

**ISBN:**364200332X

**Category:**Mathematics

**Page:**258

**View:**5464

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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*

**Author**: Heinrich von Weizsäcker

**Publisher:**Springer-Verlag

**ISBN:**3663139239

**Category:**Mathematics

**Page:**332

**View:**5208

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## Dirichlet Forms and Analysis on Wiener Space

**Author**: Nicolas Bouleau,Francis Hirsch

**Publisher:**Walter de Gruyter

**ISBN:**311085838X

**Category:**Mathematics

**Page:**335

**View:**783

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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)

## Elektronentheorie der Metalle

**Author**: A. Sommerfeld,H. Bethe

**Publisher:**Springer-Verlag

**ISBN:**3642950027

**Category:**Science

**Page:**290

**View:**9167

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## Börsenerfolg ist kein Zufall

*die besten Investmentstrategien für das neue Jahrtausend*

**Author**: Burton G. Malkiel

**Publisher:**FinanzBuch Verlag

**ISBN:**9783932114342

**Category:**Investments

**Page:**411

**View:**1429

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## Begriffsschrift und andere Aufsätze

*Mit E. Husserls und H. Scholz' Anmerkungen herausgegeben von Ignacio Angelelli*

**Author**: Gottlob Frege

**Publisher:**Georg Olms Verlag

**ISBN:**3487006235

**Category:**Philosophy

**Page:**124

**View:**5907

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Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively.

## Einführung in die kommutative Algebra und algebraische Geometrie

**Author**: Ernst Kunz

**Publisher:**Springer-Verlag

**ISBN:**3322855260

**Category:**Mathematics

**Page:**239

**View:**2639

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## Stochastik

*Einführung in die Wahrscheinlichkeitstheorie und Statistik*

**Author**: Hans-Otto Georgii

**Publisher:**Walter de Gruyter GmbH & Co KG

**ISBN:**3110386860

**Category:**Mathematics

**Page:**448

**View:**9016

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Due to the extremely positive reception of this textbook, it is now being published in its 5th edition. The book provides an introduction to the key ideas and elements of probability theory and statistics. Stochastic concepts, models, and methods are highlighted through typical application examples, then analyzed theoretically and systematically explored.

## Numerical Solution of Stochastic Differential Equations with Jumps in Finance

**Author**: Eckhard Platen,Nicola Bruti-Liberati

**Publisher:**Springer Science & Business Media

**ISBN:**364213694X

**Category:**Mathematics

**Page:**856

**View:**8739

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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.