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Convergence of Brownian motion with a scaled Dirac delta potential

Part of: Groups and semigroups of linear operators, their generalizations and applications Other generalizations Markov processes

Published online by Cambridge University Press:  23 February 2012

Florian Conrad ,
Martin Grothaus ,
Janna Lierl  and
Olaf Wittich
Florian Conrad
Affiliation:
Mathematics Department, University of Kaiserslautern, PO Box 3049, 67653 Kaiserslautern, Germany (grothaus@mathematik.uni-kl.de) Mathematics Department, Bielefeld University, PO Box 100131, 33501 Bielefeld, Germany (fconrad@math.uni-bielefeld.de)
Martin Grothaus
Affiliation:
Mathematics Department, University of Kaiserslautern, PO Box 3049, 67653 Kaiserslautern, Germany (grothaus@mathematik.uni-kl.de)
Janna Lierl
Affiliation:
Department of Mathematics, Cornell University, 120 Malott Hall, Ithaca, NY 14853, USA (jlierl@math.cornell.edu)
Olaf Wittich
Affiliation:
Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany (olaf.wittich@matha.rwth-aachen.de)
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Abstract

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The method of deriving scaling limits using Dirichlet-form techniques has already been successfully applied to a number of infinite-dimensional problems. However, extracting the key tools from these papers is a rather difficult task for non-experts. This paper meets the need for a simple presentation of the method by applying it to a basic example, namely the convergence of Brownian motions with potentials given by n multiplied by the Dirac delta at 0 to Brownian motion with absorption at 0.

Keywords

Dirichlet formslimit theoremsstrong Feller property

MSC classification

Secondary: 47D07: Markov semigroups and applications to diffusion processes 60J60: Diffusion processes 31C25: Dirichlet spaces

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 2 , June 2012 , pp. 403 - 427
Copyright
Copyright © Edinburgh Mathematical Society 2012

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