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A Schilder Type Theorem for Super-Brownian Motion

Published online by Cambridge University Press:  20 November 2018

Klaus Fleischmann ,
Jürgen Gärtner  and
Ingemar Kaj
Klaus Fleischmann
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics Mohrenstrasse 39 D-10117 Berlin, Germany email: e-mail: fleischm@wias-berlin.de
Jürgen Gärtner
Affiliation:
Department of Mathematics Technical University Strasse des 17. Juni 136 D-10623 Berlin, Germany email: e-mail: jg@math. tu-berlin.de
Ingemar Kaj
Affiliation:
Department of Mathematics Box 480 S-751 06 Uppsala, Sweden email: e-mail: ingemar.kaj@math.uu.se
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Abstract

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Let X be a d-dimensional continuous super-Brownian motion with branching rate ε, which might be described symbolically by the "stochastic equation" a space-time white noise. A Schilder type theorem is established concerning large deviation probabilities of X on path space as ε → 0, with a representation of the rate functional via an L2 -functional on a generalized "Cameron-Martin space" of measure-valued paths.

Keywords

60J8060F1060G57Schilder's Theoremsuper-Brownian motionsuperprocesslarge deviationsrate functionalCameron-Martin spacecumulant equationcomplete blow-up
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 3 , 01 June 1996 , pp. 542 - 568
Copyright
Copyright © Canadian Mathematical Society 1996

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