 Small-time expansions for the transition distributions of Lévy processesJosé E. Figueroa-López and Christian Houdré Stochastic Processes and their Applications, 2009, vol. 119, issue 11, 3862-3889 Abstract: Let X=(Xt)t>=0 be a Lévy process with absolutely continuous Lévy measure [nu]. Small-time expansions of arbitrary polynomial order in t are obtained for the tails , y>0, of the process, assuming smoothness conditions on the Lévy density away from the origin. By imposing additional regularity conditions on the transition density pt of Xt, an explicit expression for the remainder of the approximation is also given. As a byproduct, polynomial expansions of order n in t are derived for the transition densities of the process. The conditions imposed on pt require that, away from the origin, its derivatives remain uniformly bounded as t-->0. Such conditions are then shown to be satisfied for symmetric stable Lévy processes as well as some tempered stable Lévy processes such as the CGMY one. The expansions seem to correct the asymptotics previously reported in the literature. Keywords: Lévy; processes; Small-time; expansions; of; distributions; Transition; distributions; Transition; densities; estimates (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:119:y:2009:i:11:p:3862-3889 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.