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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


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


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


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


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


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.


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


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


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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