2022
DOI: 10.48550/arxiv.2202.05919
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Almost Sure Uniform Convergence of Stochastic Processes in the Dual of a Nuclear Space

Abstract: Let Φ be a nuclear space and let Φ ′ denote its strong dual. In this paper we introduce sufficient conditions for the almost surely uniform convergence on bounded intervals of time for a sequence of Φ ′ -valued processes having continuous (respectively càdlàg) paths. The main result is formulated first in the general setting of cylindrical processes but later specialized to other situations of interest. In particular, we establish conditions for the convergence to occur in a Hilbert space continuously embedded… Show more

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