Iscoe, I.; Marcus, M. B.; McDonald, D.; Talagrand, M.; Zinn, J. Continuity of \(\ell ^ 2\)-valued Ornstein-Uhlenbeck processes. (English) Zbl 0699.60052 Ann. Probab. 18, No. 1, 68-84 (1990). The authors consider the almost-sure continuity of the following \(\ell^ 2\)-valued Ornstein-Uhlenbeck process given by \[ dX_ t=AX_ tdt+\sqrt{2\alpha}dB_ t, \] where A is a positive, self-adjoint operator on \(\ell^ 2\), \(B_ t\) is a cylindrical Brownian motion on \(\ell^ 2\) and \(\alpha\) is a positive diagonal operator on \(\ell^ 2\). They give a simple sufficient condition for the almost-sure continuity of \(X_ t\) in \(\ell_ 2\) and show that it is quite sharp. Furthermore, they obtain necessary and sufficient conditions in special cases. Reviewer: R.Curtain Cited in 23 Documents MSC: 60H20 Stochastic integral equations 60G15 Gaussian processes 60G17 Sample path properties Keywords:stochastic evolution equations; almost-sure continuity; Ornstein- Uhlenbeck process PDFBibTeX XMLCite \textit{I. Iscoe} et al., Ann. Probab. 18, No. 1, 68--84 (1990; Zbl 0699.60052) Full Text: DOI