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

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

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.

Keywords

  • Supremum
  • Random Sum
  • Chain Argument
  • Tail Distribution
  • Gaussian Random Variables

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© 2013 Springer-Verlag Berlin Heidelberg

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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

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