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Random Processes in Physics and Finance

Melvin Lax, Wei Cai, and Min Xu

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book discusses random processes in physics, from basic probability theory to the Fokker-Planck process and Langevin equation for the Fokker Planck process and diffusion. It includes diverse ... More


Stochastic Modeling and Analysis

Richard M. Murray

in Biomolecular Feedback Systems

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161532
eISBN:
9781400850501
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161532.003.0004
Subject:
Biology, Biochemistry / Molecular Biology

This chapter explores stochastic behavior in biomolecular systems. It does so by first building on the preliminary discussion of stochastic modeling laid out in Chapter 2. The chapter reviews methods ... More


Population Density Methods in Large-Scale Neural Network Modelling

Daniel Tranchina

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0007
Subject:
Mathematics, Biostatistics

Population density methods have a rich history in theoretical and computational neuroscience. In earlier years, these methods were used in large part to study the statistics of spike trains. Starting ... More


Statistical Models of Spike Trains

Liam Paninski, Emery N. Brown, Satish Iyengar, and Robert E. Kass

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0010
Subject:
Mathematics, Biostatistics

Spiking neurons make inviting targets for analytical methods based on stochastic processes: spike trains carry information in their temporal patterning, yet they are often highly irregular across ... More


Men and Machines: Service Attachés as Procurers of Information on Personnel and Materiel

Matthew S. Seligmann

in Spies in Uniform: British Military and Naval Intelligence on the Eve of the First World War

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199261505
eISBN:
9780191718618
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199261505.003.0004
Subject:
History, Military History

This chapter examines the intelligence information supplied by the service attachés on technical military and naval matters. It demonstrates that a great deal of useful and accurate information was ... More


Large-scale collective motion at finite thermal excitations

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0011
Subject:
Physics, Nuclear and Plasma Physics

This chapter uses a Kramers-Moyal expansion to derive from short time propagators transport equations of Fokker-Planck type for global motion. Because of the inherent non-linearities, the transport ... More


Heavy-ion collisions at low energies

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0013
Subject:
Physics, Nuclear and Plasma Physics

In this regime heavy ion collisions can be parameterized by shape variables, the evolution of which is determined by transport equations of Fokker-Planck or Langevin type. This chapter describes ... More


Properties of Langevin and Fokker–Planck equations

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0025
Subject:
Physics, Nuclear and Plasma Physics

This chapter introduces Langevin- and Fokker-Planck equations by way of a heuristic approach to the physics of Brownian particles. Variances of physical quantities are defined and related to ... More


Generalized Fokker–Planck equation

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/9780198567769.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Thermal noise and Gaussian noise sources combine to create a category of Markovian processes known as Fokker–Planck processes. This chapter discusses Fokker–Planck processes such as ... More


The master equation

J. C. Garrison and R. Y. Chiao

in Quantum Optics

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198508861
eISBN:
9780191708640
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508861.003.0019
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter examines the evolution of an open system — the sample — with the quantum Liouville equation for the world density operator. The fundamental approximation is that the action of the sample ... More


IDEAL CHAIN MODELS

Glenn H. Fredrickson

in The Equilibrium Theory of Inhomogeneous Polymers

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567295
eISBN:
9780191717956
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567295.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses elementary statistical mechanical models of ideal chains, i.e., polymers in isolation and not experiencing interactions with other polymers. Freely jointed and bead-spring ... More


SINGLE CHAINS IN EXTERNAL FIELDS

Glenn H. Fredrickson

in The Equilibrium Theory of Inhomogeneous Polymers

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567295
eISBN:
9780191717956
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567295.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines the subject of polymers experiencing external potential fields that vary in space. The statistical mechanical problem is reduced to the solution of Fokker-Planck equations, and ... More


Introduction to condensed-phase dynamics

Niels E. Henriksen and Flemming Y. Hansen

in Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199203864
eISBN:
9780191708251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199203864.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses chemical reactions in solution; first, how solvents modify the potential energy surface of the reacting molecules, and second the role of diffusion. As a first approximation, ... More


Stochastic Differential Equations: Langevin, Fokker–Planck Equations

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses Langevin equations, that is, stochastic differential equations related to diffusion processes, brownian motion, or random walk. From the Langevin equation, the Fokker–Planck ... More


Langevin treatment of the Fokker–Planck process

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/9780198567769.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the Langevin treatment of the Fokker–Planck process and diffusion. The form of Langevin equation used is different from the stochastic differential equation using Ito's ... More


The rotating wave van del Pol oscillator (RWVP)

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/9780198567769.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explains why a laser line is so narrow (it can be as low as one cycle per second, even when the laser frequency is of the order of 10 per second) and shows that autonomous oscillators ... More


STOCHASTIC PROCESSES

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter extends the ideas of Chapter 2 by introducing the notion of stochastic process or random process and its distribution functions. The idea of a Markov process is defined. The ... More


THE SMOLUCHOWSKI EQUATION

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the Smoluchowski equation, a configuration space description of a Brownian particle in a field of force. It begins with the Kramers–Klein equation, essentially the ... More


Classical Probability Theory and Stochastic Processes

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/9780199213900.003.01
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter contains a survey of classical probability theory and stochastic processes. It starts with a description of the fundamental concepts of probability space and Kolmogorov axioms. These ... More


PATH INTEGRALS AND QUANTIZATION

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter constructs path integrals for general Hamiltonians with potentials linear in the velocities, like Hamiltonians of particles in a magnetic field. Two examples are considered: a quantum ... More


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