This is a preview of subscription content, log in via an institution to check access.
Literature Cited
Z. Zychlik and D. Szynal, “On the limit behavior of the sums of a random number of independent random variables,” Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys.,20, No. 5, 401–406 (1972); Colloq. Math.,28, No. 1, 147–159 (1973).
Rao B. L. S. Prakasa, “Limit theorems for random number of random elements in complete separable metric spaces,” Acta Math. Sci. Hung.,24, Nos. 1–2 (1974).
J. Rosinski, “Limit theorems for randomly indexed sums of random vectors,” Colloq. Math.,34, No. 1, 91–107 (1975).
L. Berzhnitskas, V. Bernotas, and V. I. Paulauskas, “Estimate of speed of convergence in limit theorems for the sum of a random number of independent random vectors,” Liet. Mat. Rinkinys,13, No. 3, 53–61 (1973).
V. I. Paulauskas, “On the sum of a random number of multidimensional random vectors,” Liet. Mat. Rinkinys,12, No. 2, 109–131 (1972).
V. I. Paulauskas, “On closeness of distributions of two sums of independent random vectors with values in a Hilbert space,” Liet. Mat. Rinkinys,15, No. 3, 177–200 (1975).
V. I. Paulauskas, “Nonuniform estimates in the central limit theorem in Hilbert space,” Liet. Mat. Rinkinys,15, No. 4, 177–190 (1975).
V. I. Paulauskas, “On speed on convergence in the central limit theorem in some Banach spaces,” (in press).
E. I. Ostrovskii, “Gaussian semigroups in Banach space,” Teor. Veroyatn Ee Primen.,20, No. 2, 447–450 (1975).
I. Tomko, “On the estimate of the remainder term in the central limit theorem for the sum of a random quantity of terms,” Teor. Veroyatn. Ee Primen.,16, No. 1, 164–171 (1971).
Additional information
V. Kapsukas Vilnius State University. Translated from Lietuvos Matematikos Rinkinys (Litovskii Matematicheskii Sbornik), Vol. 17, No. 3, pp. 17–27, July–September 1977.
Rights and permissions
About this article
Cite this article
Bernotas, V. Sums of a random number of random variables with values in Hilbert space. Lith Math J 17, 297–305 (1977). https://doi.org/10.1007/BF01053919
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01053919