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We show that the uniform norm of generalized grey Brownian motion over theunit interval has an analytic density, excluding the special case of fractionalBrownian motion. Our main result is an asymptotic expansion for the small ballprobability of generalized grey Brownian motion, which extends to other normson path space. The decay rate is not exponential but polynomial, of degree two.For the uniform norm and the H\"older norm, we also prove a large deviationsestimate.

Small ball probabilities and large deviations for grey Brownian motion