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Stochastic Population ProcessesAnalysis, Approximations, Simulations$
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Eric Renshaw

Print publication date: 2011

Print ISBN-13: 9780199575312

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199575312.001.0001

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Markov processes in continuous time and space

Markov processes in continuous time and space

Chapter:
(p.295) 6 Markov processes in continuous time and space
Source:
Stochastic Population Processes
Author(s):

Eric Renshaw

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199575312.003.0006

Having dealt with processes in discrete space, and discrete and continuous time, this chapter investigates Markov processes in continuous space and time. It follows a natural progression through the Wiener process, the Fokker–Planck diffusion equation and the Ornstein–Uhlenbeck process, and tracks the relationships between them. When barriers are introduced theoretical development is not straightforward, so care needs to be taken when constructing solutions.

Keywords:   Markov process, Wiener process, Fokker–Planck diffusion equation, Ornstein–Uhlenbeck process

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