On a certain exponential inequality for Gaussian processes

摘要

If X = (X_j)_(j=1)~m is a zero-mean Gaussian stochastic process and σ_j = (E[X_j~2])~(1/2), j=1,..., m, Tsirel'son (Theory Probab. Appl., 30, 820-828, 1985) and more explicitly Vitale (Ann. Probab., 24, 2172-2178, 1996 and A log-concavity proof for a Gaussian exponential bound. In: Hill, T.P., Houdre, C. (eds.) Advances in Stochastic Inequalities, Contemporary Mathematics, vol. 234, pp. 209-212.