Asymptotical behavior of partial integral-differential equation on nonsymmetric layered stable processes
Junjun Kang, Yanbin Tang · Asymptotic Analysis · 2017
In this paper we consider the asymptotical behavior of the density function of one dimensional nonsymmetric layered stable processes via Lévy–Khinchin exponent. For the corresponding parabolic partial integro-differential equation [Formula: see text] generated by the Lévy operator L, the infinitesimal generator of the layered stable process, we first develop a new analytical method to instead of the usual probability method, then we give the long-time and the short-time asymptotical behavior of the solutions to the corresponding Cauchy problem of the equation [Formula: see text] respectively, and these imply the asymptotical behavior of transition density. Finally we localize the parabolic partial integro-differential equation to the bounded domains and give the error estimates due to the localization.