In this paper we introduce a self-similar Gaussian process called the generalized sub-fractional Brownian motion. This process generalizes the well-known sub-fractional Brownian motion introduced by Bojdecki et al. [5]. We prove the existence and the joint continuity of the local time of our process. We use the concept of local nondeterminism for Gaussian process introduced by Berman [4] and the analytic method used by Berman [3] for the calculation of the moments of local time.
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