A Note on Maximal Inequality for Stochastic Convolutions

Abstract

Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution

$$\int_0^t {S(t - s)} \psi (s){\text{d}}W(s)$$

driven by a Wiener process W in a Hilbert space in the case when the semigroup S(t) is of contraction type.