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Stochastic Methods in Neuroscience

Carlo Laing and Gabriel J Lord (eds)

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.001.0001
Subject:
Mathematics, Biostatistics

We give a brief introduction to modelling in mathematical neuroscience, to stochastic processes, and stochastic differential equations as well as an overview of the book.


Numerical Methods for Structured Markov Chains

Dario A. Bini, Guy Latouche, and Beatrice Meini

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.001.0001
Subject:
Mathematics, Numerical Analysis

The book deals with the numerical solution of structured Markov chains which include M/G/1 and G/M/1-type Markov chains, QBD processes, non-skip-free queues, and tree-like stochastic processes and ... More


Mathematical Preliminaries

Partha P. Mitra and Hemant Bokil

in Observed Brain Dynamics

Published in print:
2007
Published Online:
May 2009
ISBN:
9780195178081
eISBN:
9780199864829
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195178081.003.0005
Subject:
Neuroscience, Techniques, Molecular and Cellular Systems

This chapter reviews a broad range of mathematical topics relevant to the rest of the book. It begins with a brief discussion of real and complex numbers and elementary real and complex functions, ... 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


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


Stochastic Integrals

Tomas Björk

in Arbitrage Theory in Continuous Time

Published in print:
2004
Published Online:
October 2005
ISBN:
9780199271269
eISBN:
9780191602849
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199271267.003.0004
Subject:
Economics and Finance, Financial Economics

This chapter discusses the modelling of asset prices as continuous time stochastic processes. Diffusion processes and stochastic differential equations are used as building blocks to obtain the most ... More


A Brief Introduction to Some Simple Stochastic Processes

Benjamin Lindner

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/9780199235070.003.0001
Subject:
Mathematics, Biostatistics

This chapter gives an overview of simple continuous, two-state, and point processes playing a role in theoretical neuroscience. First, various characteristics of these stochastic processes are ... 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


Time Series Analysis

Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter summarizes the fundamental concepts and tools for analyzing time series data. Time series analysis is a branch of applied mathematics developed mostly in the fields of signal processing ... More


Systematically Interrogating Agent-Based Models

Michael Laver and Ernest Sergenti

in Party Competition: An Agent-Based Model

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691139036
eISBN:
9781400840328
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691139036.003.0004
Subject:
Political Science, Comparative Politics

This chapter develops the methods for designing, executing, and analyzing large suites of computer simulations that generate stable and replicable results. It starts with a discussion of the ... More


Introduction

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/9780199575312.003.0001
Subject:
Mathematics, Applied Mathematics, Mathematical Biology

This introductory chapter presents a summary of the topics covered which not only provides a road map to specific content but also highlights the strong relationships which exist between the various ... More


Representing Response Times as Random Variables

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/9780195070019.003.0001
Subject:
Psychology, Cognitive Models and Architectures

This chapter begins with a discussion of the study of response times. Response times are treated as observations of a random variable. The mathematics of stochastic processes is then used to ... More


Econometric Concepts

David F. Hendry

in Dynamic Econometrics

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198283164
eISBN:
9780191596384
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283164.003.0002
Subject:
Economics and Finance, Econometrics

The main concepts for empirical modelling of economic time series are explained: parameter and parameter space; constancy; structure; distributional shape; identification and observational ... 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


Spatial processes

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/9780199575312.003.0009
Subject:
Mathematics, Applied Mathematics, Mathematical Biology

All the previous analyses are based on the assumption that populations develop at a single site where individuals mix homogeneously. Whilst this is mathematically ideal, in that it facilitates ... More


What is a random 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/9780198567769.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A random or stochastic process is a random variable that evolves in time by some random mechanism (of course, the time variable can be replaced by a space variable, or some other variable, in ... 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


Introduction and Overview

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:
10.1093/0198288107.003.0001
Subject:
Economics and Finance, Econometrics

Serves as an introductory overview for the rest of the book, and outlines its main aims. As a basis for the following chapters, an overview and clarification of equilibrium relationships in economic ... 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


Aspiration-based Adaptive Rules

Jonathan Bendor, Daniel Diermeier, David A. Siegel, and Michael M. Ting

in A Behavioral Theory of Elections

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691135076
eISBN:
9781400836802
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691135076.003.0002
Subject:
Political Science, American Politics

This chapter discusses some general properties of aspiration-based adaptive rules (ABARs). It begins with an overview of propensity and aspiration-based adjustment, using axioms to represent three ... More


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