Summary
Let E′ be the dual of a nuclear Fréchet space E (of which the Schwartz space ℒ(ℝd) of tempered distributions is one). We give a simple sufficient condition for the strong continuity of a weakly continuous E′-valued stochastic process and as applications examine the Kolmogorov-Hahn-Delporte criteria.
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Mitoma, I. Continuity of stochastic processes with values in the dual of a nuclear space. Z. Wahrscheinlichkeitstheorie verw Gebiete 63, 271–279 (1983). https://doi.org/10.1007/BF00538966
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DOI: https://doi.org/10.1007/BF00538966