An Extension of Sub-Fractional Brownian Motion

Abstract

In this paper, firstly, we introduce and study a self-similar Gaussian process with parameters $H \in{(0,1)}$ and $K \in(0,1]$ that is an extension of the well known sub-fractional Brownian motion introduced by Bojdecki et al. Secondly, by using a decomposition in law of this process, we prove the existence and the joint continuity of its local time