This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Babu, G. J. and Ghosh, M., A random functional central limit theorem for martingales, Acta Math. Acad. Sci. Hung., 27(1976), 301–306.
Billingsley, P., Convergence of Probability Measures, New York, 1968.
Borisov, I. S., On the rate of convergence for distributions of of integral type functionals, Teor. Verojatn. i Primenen., 21(1976), 293–308.
Brown, B. M., Martingale central limit theorems, Ann. Math. Statist., 42(1971), 59–66.
Burkholder, D. L., Martingale transforms, Ann. Math. Statist., 37(1966), 1494–1504.
Hall, P., The convergence of moments in the martingale central limit theorems, Z. Wahrsch. Verw. Gebiete, 44(1978), 253–260.
Heyde, C. C. and Brown, B. M., On the departure from normality of a certain class of martingales, Ann. Math. Statist., 41(1970), 2161–2165.
O’Reilly, N. E., On Sawyer’s rates of convergence for some functionals in probability, Ann. Probability, 2(1974), 1179–1184.
Petrov, V. V., Sums of Independent Random Variables, Berlin-Heidelberg-New York, 1975.
Rychlik, Z., Martingale random central limit theorems, Acta Math. Acad. Sci. Hung., 34(1979), 129–139.
Sawyer, S., Rates of convergence for some functionals, Ann. Math. Statist., 43(1972), 273–284.
Strassen, V., Almost sure behaviour of sums of independent random variables and martingales, Proc. FifthBerkeley Symp. Math. Statist. Prob., 2(1967), 315–343.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Rychlik, Z., Szyszkowski, I. (1984). On the rate of convergence for distributions of integral type functionals. In: Szynal, D., Weron, A. (eds) Probability Theory on Vector Spaces III. Lecture Notes in Mathematics, vol 1080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099801
Download citation
DOI: https://doi.org/10.1007/BFb0099801
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13388-9
Online ISBN: 978-3-540-38939-2
eBook Packages: Springer Book Archive
