## 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.

## 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

## 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

## 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