Geodesic
On weak convergence of finite-dimensional and infinite-dimensional distributions of random processes
Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 1-11.

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We study conditions on metrics on spaces of measurable functions under which weak convergence of Borel probability measures on these spaces follows from weak convergence of finite-dimensional projections of the considered measures.
Keywords: Convergence in measure, weak convergence, finite-dimensional distributions. 
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V. I. Bogachev; A. F. Miftakhov. On weak convergence of finite-dimensional and infinite-dimensional distributions of random processes. Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a0/

[1] A. N. Baushev, “On the weak convergence of probability measures in Orlicz spaces”, Theory Probab. Appl., 40:3 (1995), 420–429 | DOI | MR

[2] A. N. Baushev, “On the weak convergence of probability measures in a Banach space”, J. Math. Sci., 109:6 (2002), 2037–2046 | DOI | MR

[3] P. Billingsley, Convergence of probability measures, Wiley, New York, 1968 | MR | Zbl

[4] V. I. Bogachev, Measure theory, v. 1, 2, Springer, New York, 2007 | MR | Zbl

[5] Russian Math. Surveys., 67:5, 785–890 | DOI | DOI | MR | Zbl

[6] V. I. Bogachev, N. V. Krylov, M. Röckner, S. V. Shaposhnikov, Fokker–Planck–Kolmogorov equations, Amer. Math. Soc., Providence, Rhode Island, 2015 | MR | Zbl

[7] Russian Math. Surveys., 31:2, 1–69 | DOI | MR | Zbl

[8] Theory Probab., 18:4 (1973) | MR | Zbl

[9] H. Cremers, D. Kadelka, “On weak convergence of stochastic processes with Lusin path spaces”, Manuscripta Math., 45 (1984), 115–125 | DOI | MR | Zbl

[10] H. Cremers, D. Kadelka, “On weak convergence of integral functionals of stochastic processes with applications to processes taking paths in $L_p^E$”, Stoch. Processes Appl., 21 (1986), 305–317 | DOI | MR | Zbl

[11] R. M. Dudley, Real analysis and probability, Wadsworth Brooks, Pacific Grove, California, 1989 | MR | Zbl

[12] R. Fortet, E. Mourier, “Convergence de la répartition empirique vers la répartition théorique”, Ann. Sci. l'École Norm. Sup., 70:3 (1953), 267–285 | MR | Zbl

[13] v. 1, Moscow, 1971 | Zbl

[14] L. Š. Grinblat, “A limit theorem for measurable random processes and its applications”, Proc. Amer. Math. Soc., 61 (1976), 371–376 | DOI | MR

[15] L. Š. Grinblat, “Convergence of probability measures on separable Banach spaces”, Proc. Amer. Math. Soc., 67 (1977), 321–323 | DOI | MR

[16] L. Š. Grinblat, “Convergence of measurable random functions”, Proc. Amer. Math. Soc., 74 (1979), 322–325 | DOI | MR

[17] Ukrainian Math. J., 32:1, 19–25 | DOI | MR | Zbl | Zbl

[18] L. V. Kantorovich, G. Sh. Rubinstein, “On a space of completely additive functions”, Vestnik Leningrad. Univ., 13:7 (1958), 52–59 (in Russian) | MR | Zbl

[19] L. Le Cam, “Convergence in distribution of stochastic processes”, Univ. Calif. Publ. Statist., 2 (1957), 207–236 | MR | Zbl

[20] P. A. Meyer, W. A. Zheng, “Tightness criteria for laws of semi-martingales”, Annales l'Inst. H. Poincaré, 20:4 (1984), 353–372 | MR | Zbl

[21] R. P. Pakshirajan, “A note on the weak convergence of probability measures in the $D[0,1]$ space”, Statist. Probab. Lett., 78:6 (2008), 716–719 | DOI | MR | Zbl

[22] D. Pollard, Convergence of stochastic processes, Springer, Berlin – New York, 1984 | MR | Zbl

[23] R. Rebolledo, “Topologie faible et méta-stabilité”, Séminaire de probabilités XXI, Lecture Notes in Math., 1247, 1987, 545–562 | MR

[24] H. Sadi, “Une condition nécessaire et suffisante pour la convergence en pseudo-loi des processus”, Séminaire de probabilités XXII, Lecture Notes in Math., 1321, 1988, 434–437 | DOI | MR | Zbl

[25] H. Tsukahara, “On the convergence of measurable processes and prediction processes”, Illinois J. Math., 51:4 (2007), 1231–1242 | MR | Zbl

[26] A. W. van der Vaart, J. A. Wellner, Weak convergence and empirical processes. With applications to statistics, Springer-Verlag, New York, 1996 | MR | Zbl