## 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