A Note on Maximal Inequality for Stochastic Convolutions

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.

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