Large deviations for discontinuous additive functionals of symmetric stable processes

✍ Scribed by Masayoshi Takeda; Kaneharu Tsuchida

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 227 KB
• Volume: 284
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200810843

✦ Synopsis

Abstract

Let X~t~ be a symmetric stable process on d‐dimensional Euclidean space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {R}}^d$\end{document}. Let F(x, y) be a symmetric positive bounded function on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {R}}^d\times {\mathbb {R}}^d$\end{document} vanishing on the diagonal set and define a discontinuous additive functional by A~t~(F) = ∑~0 < s ⩽ t~F(X~s −~, X~s~). We establish the large deviation principle of A~t~(F)/t by employing the Gärtner‐Ellis theorem. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim