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In this paper we establish a change-of-variable formula for a class of Gaussian processes with a covariance function satisfying minimal regularity and integrability conditions. The existence of the local time and a version of Tanaka’s formula are derived. These results are applied to a general class of self-similar processes that includes the bifractional Brownian motion. On the other hand, we establish a comparison result on the Laplace transform of the hitting time for a fractional Brownian motion with Hurst parameter H < 1 2 .

Stochastic calculus for Gaussian processes and application to hitting times