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Stochastic Methods in Neuroscience$
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Carlo Laing and Gabriel J Lord

Print publication date: 2009

Print ISBN-13: 9780199235070

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199235070.001.0001

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A Brief Introduction to Some Simple Stochastic Processes

A Brief Introduction to Some Simple Stochastic Processes

Chapter:
(p.1) 1 A Brief Introduction to Some Simple Stochastic Processes
Source:
Stochastic Methods in Neuroscience
Author(s):

Benjamin Lindner

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199235070.003.0001

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 introduced such as probability densities, moments, correlation functions, the correlation time, and the noise intensity of a process. Then analytical and numerical methods to calculate or compute these various statistics are explained and illustrated by means of simple examples (Ornstein–Uhlenbeck process, random telegraph noise, Poissonian shot noise). Further, useful relations among the different statistics (Wiener–Khinchin theorem, relations between spectral and interval statistics of point processes) are also discussed.

Keywords:   stochastic process, point process, dynamical noise, analytical methods

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