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Continuity of trajectories of Gaussian chaoses of finite degree. (Continuité des trajectoires des chaos gaussiens de degré fini.) (French) Zbl 0868.60040

Summary: We extend a theorem due to X. Fernique [ibid. 15, 291-300 (1995; Zbl 0861.60046)]: let \(X\) be a Gaussian real chaos of finite degree on a metric compact set \(T\). Suppose that \(X\) is continuous in probability and a.s. continuous along \(\mathcal D\), where \(\mathcal D\) is a countable dense subset of \(T\). Then \(X\) has a modification with continuous paths. This result is obtained by using decoupling methods [see M. A. Arcones and E. Giné, J. Theor. Probab. 6, No. 1, 101-122 (1993; Zbl 0785.60023)], integrability properties for homogeneous Gaussian chaos and numerical oscillations of random functions [see K. Itô and M. Nisio, Math. Scand. 22, 209-223 (1968; Zbl 0231.60027)].

MSC:

60G17 Sample path properties