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References
Badrikian, A.: Remarkes sur les Théorèmes de Bochner et P. Lévy. Lecture Notes in Math. No. 31. Berlin-Heidelberg-New York: Springer 1967.
Horváth, J.: Topological vector spaces and distributions, 1. Massachusetts-Palo Alto-London-Don Mills, Ontario: Addison-Wesley 1966.
Itô, K.: Continuous additive ℒ’-processes. Lecture Notes in Control and Infor. Sci. 25. Berlin-Heidelberg-New York: Springer 1980.
_____: Various problems for stochastic differential equations on infinite dimensional vector spaces. Kokyuroku, RIMS, Kyoto Univ. 391, 91–107 (1980). (in Japanese).
Itô, K and Nisio, M.: On the convergence of sums of independent Banach space valued random variables. Osaka J. Math. 5, 35–48 (1968).
Köthe, G.: Topological vector spaces 1. Berlin-Heidelberg-New York: Springer 1969.
Martin-Löf, A.: Limit theorems for the motion of a Poisson system of independent Markovian particles with high density. Z. Wahrscheinlichkeitstheorie verw. Gebiete 34, 205–223 (1976).
Mitoma, I.: On the norm continuity of ℒ’-valued Gaussian processes. Nagoya Math. J. 82, 209–220 (1981).
_____: Continuity of stochastic processes with values in the dual of a nuclear space. To appear in Z. Wahrscheinlichkeitstheorie verw. Gebiete.
_____: On the sample continuity of ℒ’-processes. (submitted).
_____: Tightness of probabilities on C([0, 1]; ℒ’) and D([0,1]; ℒ’). (submitted).
Tanaka, H and Hitsuda, M.: Central limit theorem for a simple diffusion model of interacting particles. Hiroshima Math. J. 11, 415–423 (1981).
Xia, D.: Measure and integration theory on infinite-dimensional spaces. New York and London: Academic Press 1972.
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© 1983 Springer-Verlag Berlin Heidelberg
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Mitoma, I. (1983). Almost sure uniform convergence of continuous stochastic processes with values in the dual of a nuclear space. In: Prokhorov, J.V., Itô, K. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072939
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DOI: https://doi.org/10.1007/BFb0072939
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