Abstract
In recent papers Bezandry and Fernique (1990), 1992), Fernique (1993) have given new convergence and tightness criteria for random processes whose sample paths are right-continuous and have left-limits. These criteria have been applied by Bezandry and Fernique, Bloznelis and Paulauskas to prove the central limit theorem (CLT) in the Skorohod space D[0,1].
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References
Bentkus V., Goetze F., Paulauskas V and A. Račkauskas (1990) The Accuracy of Gaussian Approximation in Banach Spaces. Bielefeld University SFB Preprint N 100.
Bezandry P.H. and X. Fernique (1990). Analyse de fonctions aleatoires peu regulieres sur [0,1]. C. R. Acad. Sci Paris, 310, I, 745–750.
Bezandry P.H. and X. Fernique (1992). Sur la propriete de la limite centrale dans D[0,1]. Ann. Inst. Henri Poincare, 28, 1, 31–46.
Bickel P.J. and M.J. Wichura (1971). Convergence criteria for multiparameter stochastic processes and some applications. Ann. Statist. 42, 1656–1670.
Billingsley P.(1968). Convergence of Probability Measures. Wiley, New York.
Bloznelis M. and V. Paulauskas (1993). A note on the central limit theorem for stochastically continuous processes. Stock. Proc. Appl., to appear.
Centsov N.N. (1956). Vinerovskie slucainye polia ot neskolkich parametrov. Doklady AN USSR, T. 106, N 4, 607–609.
Fernique X. (1964). Continuite des processus gaussiens. C.R. Acad. Sci. Paris, 258, 6058–6060.
Fernique X. (1993). Les fonctions aleatoires cadlag, la compacite de leurs lois. Preprint.
Hahn M. (1977). A note on the central limit theorem for square-integrable processes. Proc. Amer. Math. Soc., 64, 331–334.
Hahn M. (1978). Central limit theorem in D[0,1]. Z. Wahr, verw. Gebiete, 44, 89–101.
Klamkin M.S. (1976). On some multiple integrals. J. Math.Analysis Appl., 54, 476–479.
Kuelbs J. (1973). The invariance Principle for Banach space valued random variables. J. Multivar. Analysis, 3, 161–172.
Lachout P. (1988). Billingsley-type tightness criteria for multiparameter stochastic processes. Kybernetika. Academia Praha, 24, 5, 363–371.
Neuhaus G. (1971). On weak convergence of stochastic processes with multidimensional time parameter. Ann. Probab., 42, 1285–1295.
Straf M.L. (1972). Weak convergence of stochastic processes with several parameters. Proc. Sixth Berkeley Symp. Math. Statist. Probab., 2, 187–221.
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Bloznelis, M., Paulauskas, V. (1994). On the Central Limit Theorem for Multiparameter Stochastic Processes. In: Hoffmann-Jørgensen, J., Kuelbs, J., Marcus, M.B. (eds) Probability in Banach Spaces, 9. Progress in Probability, vol 35. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0253-0_9
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DOI: https://doi.org/10.1007/978-1-4612-0253-0_9
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