Skip to main content

The Proof of Theorems 4.1 and 4.2 on the Supremum of Random Sums

  • Chapter
  • First Online:
On the Estimation of Multiple Random Integrals and U-Statistics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2079))

  • 1219 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Publish with us

Policies and ethics