Box dimension of interpolations of self-similar processes with stationary increments

We prove that under a general condition interpolation dimensions of H-sssi process converge in probability to 2−H.The result can be applied to a wideclass of H-sssi processes which includes fractional Brownian motions, (α, β)-fractional stable processes or strictly stable H-sssi processes. Moreover, we prove that for an H-sssi process with continuous sample paths the same general condition implies uniform convergence in probability of sample paths o f fractal interpolations to sample paths of the interpolated process.