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Methods of Small Parameter in Mathematical BiologyDiffusion Limit of the Telegraph Equation

Methods of Small Parameter in Mathematical Biology: Diffusion Limit of the Telegraph Equation [In this chapter we consider asymptotic limits of correlated and uncorrelated random walks. We begin with necessary background on Sobolev spaces and analytic semigroups. The main aim of the chapter is to prove that the probabilistic densities describing correlated random walk, which are solutions of the hyperbolic telegraphers’ equation, can be approximated by solutions of a specially constructed diffusion equation which describes uncorrelated random walk.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Methods of Small Parameter in Mathematical BiologyDiffusion Limit of the Telegraph Equation

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2014
ISBN
978-3-319-05139-0
Pages
173 –194
DOI
10.1007/978-3-319-05140-6_6
Publisher site
See Chapter on Publisher Site

Abstract

[In this chapter we consider asymptotic limits of correlated and uncorrelated random walks. We begin with necessary background on Sobolev spaces and analytic semigroups. The main aim of the chapter is to prove that the probabilistic densities describing correlated random walk, which are solutions of the hyperbolic telegraphers’ equation, can be approximated by solutions of a specially constructed diffusion equation which describes uncorrelated random walk.]

Published: Mar 12, 2014

Keywords: Random walk; Diffusion

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