Stochastic integration for fractional Levy process and stochastic differential equation driven by fractional Levy noise

摘要

In this paper, based on the white noise analysis of square integrablepure-jump Levy process given by [1], we define the formal derivative offractional Levy process defined by the square integrable pure-jump Levy processas the fractional Levy noises by considering fractional Levy process as thegeneralized functional of Levy process, and then we define the Skorohodintegral with respect to the fractional Levy process. Moreover, we propose aclass of stochastic Volterra equations driven by fractional Levy noises andinvestigate the existence and uniqueness of their solutions; In addition, wepropose a class of stochastic differential equations driven by fractional Levynoises and prove that under the Lipschtz and linear conditions there existsunique stochastic distribution-valued solution.