References
P. Billingsley, Convergence of Probability Measures [Russian translation], Nauka, Moscow (1977).
A. N. Kolmogorov, Information Theory and the Theory of Algorithms [in Russian], Nauka, Moscow (1987).
Yu. V. Prokhorov, “Convergence of random processes and limit theorems in probability theory,” Teor. Veroyatnost. i Primenen.,1, No. 2, 178–238 (1956).
S. M. Prigarin, “On weak convergence of approximate models of Gaussian random fields,” in: Theory and Application of Statistical Modeling [in Russian], Nauka, Novosibirsk, 1988, pp. 31–39.
N. C. Jain and M. B. Marcus, “Central limit theorems forC(S)-valued random variables,” J. Funct. Anal.,19, No. 3, 216–231 (1975).
A. S. Frolov and N. N. Chentsov, “Use of dependent tests in the Monte Carlo method for obtaining smooth curves,” in: Proceed. Sixth All-Union Conference on Probability Theory and Mathematical Statistics [in Russian], Vil'nyus, 1962, pp. 425–437.
G. A. Mikhaîlov, Optimization of Weighted Monte Carlo Methods [in Russian], Nauka, Moscow (1987).
A. V. Voîtishek, “On differential conditions for weak convergence of stochastic estimates and models,” in: Methods of Statistical Modeling [in Russian], Nauka, Novosibirsk, 1986, pp. 35–52.
S. M. Prigarin, Approximate Modeling of Gaussian Homogeneous fields on the Basis of a Spectral Representation [in Russian], Preprint No. 876. Akad. Nauk SSSR Sibirsk. Otdel., Vychisl. Tsentr, Novosibirsk (1989).
S. M. Prigarin, “Asymptotic effectiveness of estimates in the method of dependent tests,” in: Abstracts: Eighth All-Union Conference on Monte Carlo Methods in Numerical Mathematics and Mathematical Physics. Part 1 [in Russian], Novosibirsk, 1991, pp. 94–96.
Additional information
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 1, pp. 140–144, January–February, 1993
Translated by I. G. Belinskaya
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Prigarin, S.M. Weak convergence of probability measures in the spaces of continuously differentiable functions. Sib Math J 34, 123–127 (1993). https://doi.org/10.1007/BF00971248
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DOI: https://doi.org/10.1007/BF00971248