Hitting probability of a Gaussian vector with values in a Hilbert space in a sphere of small radius

Let be a Gaussian random vector with values in a Hilbert space H. We denote by(a, z) the ball in H with center ata and of radius z. Some asymptotic formulas for I (a, z)=P (a, z), z 0, are presented in the paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 75–93, 1979.