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Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons

Stefan Adams

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0007
Subject:
Mathematics, Probability / Statistics, Analysis

Motivated by the Bose gas, this chapter introduces certain combinatorial structures. It analyses the asymptotic behaviour of empirical shape measures and of empirical path measures of N Brownian ... More


Science’s Cinematic Method: Motion Pictures and Scientific Research

Scott Curtis

in The Shape of Spectatorship: Art, Science, and Early Cinema in Germany

Published in print:
2015
Published Online:
May 2016
ISBN:
9780231134033
eISBN:
9780231508636
Item type:
chapter
Publisher:
Columbia University Press
DOI:
10.7312/columbia/9780231134033.003.0002
Subject:
Film, Television and Radio, Film

Chapter One examines use of film as a scientific research tool in three fields (human motion studies, physics, biology) in Germany from the 1880s to 1914. It argues that there is a close relationship ... More


Random Fractals

Peter Mörters

in New Perspectives in Stochastic Geometry

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.003.0008
Subject:
Mathematics, Geometry / Topology

This chapter expounds the theory of random fractals, using tree representation as a unifying principle. Applications to the fine structure of Brownian motion are discussed.


Interacting Brownian Motions and the Gross-Pitaevskii Formula

Stefan Adams and Wolfgang König

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0008
Subject:
Mathematics, Probability / Statistics, Analysis

Bose–Einstein condensation predicts that, under certain conditions (in particular extremely low temperature), all particles will condense into one state. Some of the physical background is surveyed ... More


Brownian motions on groups of matrices

Jacques Franchi and Yves Le Jan

in Hyperbolic Dynamics and Brownian Motion: An Introduction

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199654109
eISBN:
9780191745676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199654109.003.0007
Subject:
Mathematics, Mathematical Physics

This chapter is devoted to (left and right) Brownian motions on groups of matrices, which the chapter constructs as solutions to linear stochastic differential equations. The chapter establishes in ... More


Evidence for Molecules: Jean Perrin and Molecular Reality

Peter Achinstein

in The Book of Evidence

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195143898
eISBN:
9780199833023
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195143892.003.0012
Subject:
Philosophy, Philosophy of Science

Jean Perrin's argument for the existence of molecules on the basis of his 1908 experiments with Brownian motion is examined. Various interpretations of that argument, including hypothetico‐deductive, ... More


Stochastic Processes and Stochastic Calculus

Claus Munk

in Fixed Income Modelling

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199575084
eISBN:
9780191728648
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575084.003.0003
Subject:
Economics and Finance, Financial Economics

The price of an asset at a future point in time will typically be unknown, i.e. a random variable. In order to describe the uncertain evolution in the price of the asset over time, we need a ... More


Quantum Master Equations

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.03
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the fundamentals of the description of the quantum dynamics of open systems in terms of quantum master equations, together with its most important applications. Special ... More


Brownian Motion: Fluctuations, Dynamics, and Applications

Robert M. Mazo

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

Brownian motion is the incessant motion of small particles immersed in an ambient medium. It is due to fluctuations in the motion of the medium particles on the molecular scale. The name has been ... More


Uncertainty, Information, and Stochastic Processes

Claus Munk

in Financial Asset Pricing Theory

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199585496
eISBN:
9780191751790
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199585496.003.0002
Subject:
Economics and Finance, Econometrics

Uncertainty is a key component of financial markets and thus of any asset pricing theory. This chapter provides the tools from probability theory that are being used in the asset pricing models ... More


Brownian Motion in Granular Gases

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0015
Subject:
Physics, Condensed Matter Physics / Materials

This chapter analyzes Brownian motion in granular gases. Topics discusses include Boltzmann equation for the velocity distribution function of Brownian particles, Fokker–Planck equation for Brownian ... More


Weak Convergence in a Function Space

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0027
Subject:
Economics and Finance, Econometrics

This chapter applies the theory of Ch. 26 to the case of the space C of continuous functions on the unit interval. It is shown how to assign probability measures to C, and Weiner measure (Brownian ... More


Brownian Motion

Gopinath Kallianpur and P. Sundar

in Stochastic Analysis and Diffusion Processes

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199657063
eISBN:
9780191781759
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199657063.003.0002
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

After defining a Brownian motion (also known as a Wiener process), a standard one-dimensional Brownian motion is constructed by the use of Haar functions. Properties of a Brownian motion such as ... More


Kinetic Theory of Granular Gases

Nikolai V. Brilliantov and Thorsten Pöschel

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book ... More


Hyperbolic Dynamics and Brownian Motion: An Introduction

Jacques Franchi and Yves Le Jan

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199654109
eISBN:
9780191745676
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199654109.001.0001
Subject:
Mathematics, Mathematical Physics

The idea of this book is to illustrate an interplay between distinct domains of mathematics. Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group PSO(1, d) ... More


Brownian Motion and Stochastic Calculus

Kerry E. Back

in Asset Pricing and Portfolio Choice Theory

Published in print:
2017
Published Online:
May 2017
ISBN:
9780190241148
eISBN:
9780190241179
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780190241148.003.0012
Subject:
Economics and Finance, Financial Economics

Brownian motion and concepts of the Itôs calculus are explained, including total variation, quadratic variation, Levy’s characterization of Brownian motion, the Itô integral, the difference between ... More


Brownian Motion

Phil Attard

in Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199662760
eISBN:
9780191745287
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662760.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

Brownian motion is presented as a stochastic process, and as a bridge between thermodynamics and statistical mechanics. Einstein’s result for the linear growth in time of the mean square displacement ... More


The Theory of Open Quantum Systems

Heinz-Peter Breuer and Francesco Petruccione

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation, the text begins with a ... More


Basic Itô calculus

Jacques Franchi and Yves Le Jan

in Hyperbolic Dynamics and Brownian Motion: An Introduction

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199654109
eISBN:
9780191745676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199654109.003.0006
Subject:
Mathematics, Mathematical Physics

This chapter deals with the basic Itô calculus. Fundamental notions such as predictability, martingales and stopping times are introduced in the discrete case. The chapter then gives a short account ... More


Examples of Markovian processes

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Consider two physical problems describable by the same random process. The first process is the radioactive decay of a collection of nuclei. The second is the production of photoelectrons by a steady ... More


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