Keywords
- Brownian Motion
- Covariance Structure
- Invariance Principle
- Iterate Logarithm
- Independent Gaussian Random Variable
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
Berkes, István and Walter Philipp (1979), Approximation theorems for independent and weakly dependent random vectors, Annals of Probability, 7
Bhattacharya, R. N. (1978), private communication.
Bhattacharya, R. N. and R. Ranga Rao (1975), Normal approximation and asymptotic expansion, Wiley, New York.
Breiman, Leo (1968), Probability, Addison Wesley, Reading, Mass.
Dudley, R. M. (1968), Distances of probability measures and random variables, Annals Math. Stat. 39, 1563–1572.
Hartman, Philip and Aurel Wintner (1941), On the law of the iterated logarithm, Amer. J. Math. 63, 169–176.
Heinkel, B. (1979), Sur la loi du logarithme itéré pour des v.a. à valeurs dans un espace de Banach, this volume.
Kuelbs, J. (1976), A strong convergence theorem for Banach space valued random variables, Annals of Probability 5, 744–771.
Kuelbs, J. (1977), Kolmogorov’s law of the iterated logarithm for Banach space valued random variables, Illinois J. Math. 21, 784–800.
Kuelbs, J. and Walter Philipp (1977), Almost sure invariance principles for partial sums of mixing B-valued random variables, preprint.
Major, Peter (1976a), Approximation of partial sums of i.i.d.r.v.s. when the summands have only two moments, Z. Wahrscheinlichkeitstheorie verw. Geb. 35, 221–229.
Major, Peter (1976b), The approximation of partial sums of independent r.v.s., Z. Wahrscheinlichkeitstheorie verw. Geb. 35, 213–220.
Philipp, Walter (1978), Weak invariance principles for sums of B-valued random variables, preprint.
Pisier, G. (1975), Le théorème de la limit centrale et la loi du logarithme itéré dans les espace de Banach, Séminaire Maurey-Schwartz 1975–1976, Exposé III, Ecole Polytechnique, Paris.
Strassen, V. (1964), An almost sure invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie verw. Geb. 3, 211–226.
Strassen, V. (1965), The existence of probability measures with given marginals, Annals Math. Stat. 36, 423–439.
Yurinskii, V. V. (1975), A smoothing inequality for estimates of the Lévy-Prokhorov distance, Theory. Prob. Appl. 20, 1–10.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Philipp, W. (1979). Almost sure invariance principles for sums of B-valued random variables. In: Beck, A. (eds) Probability in Banach Spaces II. Lecture Notes in Mathematics, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071957
Download citation
DOI: https://doi.org/10.1007/BFb0071957
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09242-1
Online ISBN: 978-3-540-35341-6
eBook Packages: Springer Book Archive
