Abstract
In this chapter we prove Theorem 4.2, an estimate about the tail distribution of the supremum of an appropriate class of Gaussian random variables with the help of a method, called the chaining argument. We also investigate the proof of Theorem 4.1 which can be considered as a version of Theorem 4.2 about the supremum of partial sums of independent and identically distributed random variables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Major, P. (2013). The Proof of Theorems 4.1 and 4.2 on the Supremum of Random Sums. In: On the Estimation of Multiple Random Integrals and U-Statistics. Lecture Notes in Mathematics, vol 2079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37617-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-37617-7_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37616-0
Online ISBN: 978-3-642-37617-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)