How big are the increments of l^p-valued Gaussian processes?

Abstract

Let$\{ Y(t),t \geqslant 0\} = \{ X_k (t),t \geqslant 0\} _{k = 1}^\infty$ be a sequence of independent Gaussian processes with (h)$\sigma _k^2 (h) = E(X_k (t + h) - X_k (t))^2$ Put$\sigma (p,h) = \left( {\sum\limits_{k = 1}^\infty {\sigma _k^p (h)} } \right)^{1/p} ,p \geqslant 1$. The large increments forY(·) with bounded σ(p, h) are investigated. As an example the large increments of infinite-dimensional fractional Ornstein-Uhlenbeck process in I^P are given. The method can also be applied to certain processes with stationary increments.