## Stochastic Accumulation of Information in Discrete Time

*R. Duncan Luce*

### in Response Times: Their Role in Inferring Elementary Mental Organization

- Published in print:
- 1991
- Published Online:
- January 2008
- ISBN:
- 9780195070019
- eISBN:
- 9780199869879
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195070019.003.0008
- Subject:
- Psychology, Cognitive Models and Architectures

This chapter examines closely-related models for possible processes underlying choice reaction time. Topics discussed include accumulator models; random walks with boundaries; restrictions on the ... More

## Navigation and search

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the specifics of walks, navigation, and search processes in networks of various architectures and geometries. It starts with discussion of random walks on complex networks, ... More

## RANDOM WALK

*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/9780199556441.003.0009
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter introduces the idea of random walk and studies a number of simple cases to illustrate the concepts, mostly in one dimension. The symmetric Pearson walk, the biased walk, and the ... More

## The random walk

*Eric Renshaw*

### in Stochastic Population Processes: Analysis, Approximations, Simulations

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199575312
- eISBN:
- 9780191728778
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199575312.003.0004
- Subject:
- Mathematics, Applied Mathematics, Mathematical Biology

This chapter considers path analyses for random walks, which leads on to first passage and return probabilities and the Arc Sine Law. Both absorbing and reflecting barriers are considered in some ... More

## Random Walk and Mean-Reversion

*Christian Gollier*

### in Pricing the Planet's Future: The Economics of Discounting in an Uncertain World

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691148762
- eISBN:
- 9781400845408
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148762.003.0004
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter illustrates that the shape of the term structure of discount rates is determined by the way the wealth effect and the precautionary effects evolve with the time horizon. When the growth ... More

## Solving the Tower of Hanoi with Random Moves

*Max A. Alekseyev and Toby Berger*

### in The Mathematics of Various Entertaining Subjects: Research in Recreational Math

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164038
- eISBN:
- 9781400881338
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164038.003.0005
- Subject:
- Mathematics, History of Mathematics

This chapter studies solutions of the Tower of Hanoi puzzle and some of its variants with random moves, where each move is chosen uniformly from the set of the valid moves in the current state. The ... More

## Securities Markets and Their Efficiency

*Hendrik S. Houthakker and Peter J. Williamson*

### in The Economics of Financial Markets

- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780195044072
- eISBN:
- 9780199832958
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019504407X.003.0005
- Subject:
- Economics and Finance, Financial Economics

The discussion in this chapter begins with an analysis of central trading places, which looks at the economics of securities trading and the rationale for brokers and central trading places (with ... More

## Stochastic Accumulation of Information in Continuous Time

*R. Duncan Luce*

### in Response Times: Their Role in Inferring Elementary Mental Organization

- Published in print:
- 1991
- Published Online:
- January 2008
- ISBN:
- 9780195070019
- eISBN:
- 9780199869879
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195070019.003.0009
- Subject:
- Psychology, Cognitive Models and Architectures

This chapter examines closely-related models for possible processes underlying choice reaction time. The models are similar to those discussed in the preceding chapter, except that the accumulation ... More

## Special topics and interdisciplinary models

*Ralph Skomski*

### in Simple Models of Magnetism

- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780198570752
- eISBN:
- 9780191718816
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570752.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials

Atomic disorder has far-reaching consequences for the behavior of magnetic materials. It modifies the electronic structure but does not necessarily destroy ferromagnetism, as exemplified by amorphous ... More

## Mathematics of networks: An introduction to the mathematical tools used in the study of networks, tools that will be important to many subsequent developments

*M. E. J. Newman*

### in Networks: An Introduction

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199206650
- eISBN:
- 9780191594175
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199206650.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the basic theoretical tools used to describe and analyze networks, most of which come from graph theory, the branch of mathematics that deals with networks. Topics covered ... More

## Random Walks and Rapid Mixing

*Cristopher Moore and Stephan Mertens*

### in The Nature of Computation

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199233212
- eISBN:
- 9780191775079
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233212.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Random sampling is a technique for dealing with possible states or solutions having an exponentially large space. The best method of random sampling generally involves a random walk or a Markov ... More

## Properties of Integrated Processes

*Anindya Banerjee, Juan J. Dolado, John W. Galbraith, and David F. Hendry*

### in Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data

- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780198288107
- eISBN:
- 9780191595899
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198288107.003.0003
- Subject:
- Economics and Finance, Econometrics

Presents the important properties of integrated variables and sets out some of the preliminary asymptotic theories essential for the consideration of such processes. It explores the concepts of unit ... More

## Universality and the continuum limit

*Jean Zinn-Justin*

### in Phase Transitions and Renormalization Group

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the related questions of universality and macroscopic continuum limit in random systems with a large number of degrees of freedom. It first explains the notion of universality ... More

## First Steps in Random Walks: From Tools to Applications

*J. Klafter and I. M. Sokolov*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199234868
- eISBN:
- 9780191775024
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234868.001.0001
- Subject:
- Physics, Soft Matter / Biological Physics

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same ... More

## A Theory of the Decreasing Term Structure of Discount Rates

*Christian Gollier*

### in Pricing the Planet's Future: The Economics of Discounting in an Uncertain World

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691148762
- eISBN:
- 9781400845408
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148762.003.0008
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter aims to provide a unified theoretical foundation to the term structure of discount rates. To do this the chapter develops a benchmark model based on two assumptions: individual ... More

## The Central Binomial Coefficient

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0002
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter focuses on the ubiquitous central binomial coefficient and its properties. It confirms that Cn is a positive integer. The chapter covers Lagrange's identity.

## Ecological and Behavioral Approaches to Search Behavior

*David W. Stephens, Iain Couzin, and Luc-Alain Giraldeau*

### in Cognitive Search: Evolution, Algorithms, and the Brain

- Published in print:
- 2012
- Published Online:
- May 2016
- ISBN:
- 9780262018098
- eISBN:
- 9780262306003
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262018098.003.0003
- Subject:
- Sociology, Social Psychology and Interaction

This chapter offers a selective review of behavioral and ecological perspectives on search behavior. Basic results from foraging theory are presented and their relationship to search is discussed. ... More

## Metric stability for random walks (with applications in renormalization theory)

*Carlos Gustavo Moreira and Daniel Smania*

*Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)*

### in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159294
- eISBN:
- 9781400851317
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159294.003.0013
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter considers the stability of metric (measure-theoretic) properties of dynamical systems. A well-known example is that of (C²) expanding maps on the circle; this class is structurally ... More

## Standard finance theory

*NEIL F. JOHNSON, PAUL JEFFERIES, and PAK MING HUI*

### in Financial Market Complexity

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198526650
- eISBN:
- 9780191712104
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526650.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on the basics of standard finance theory. It discusses the details of a random walk and quantifying risk using volatility σ. It then looks at the hedging of risk within standard ... 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