Asymptotic evaluation of the Poisson measures for tubes around a jump curves

Xavier Bardina*, Carles Rovira^ and Samy Tindel'.

*Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona
08193 Bellaterra, Barcelona, Spain
^ Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007-Barcelona, Spain
' Département de Mathématiques, Institut Galilée - Université Paris 13,  Avenue  J. B. Clément, 93430-Villetaneuse, France.

Abstract

We find the symptotic behavior of $P(\|X-\Phi\!\leq\varepsilon)$ when $X$ is the solution of a linear stochastic differential equation driven by a Poisson process and $\Phi$ the solution of a linear differential equation driven by a pure jump function.
 
Published in: Applicationes Mathematicae, 29 (2), 145-156, 2002