Statistical Properties

Antanas Laurinčikas and Ramūnas Garunkštis
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Antanas Laurinčikas: Vilnius University
Ramūnas Garunkštis: Vilnius University

Chapter Chapter 5 in The Lerch Zeta-function, 2003, pp 71-109 from Springer

Abstract: Abstract In this chapter we will consider the weak convergence of probability measures defined by terms of Lerch zeta-functions. We will prove one-dimensional and multidimensional limit theorems on the complex plane and in the space of analytic functions. Let, for T > 0, ν T τ ( ⋯ ) = 1 T m e a s { τ ∈ [ 0 , T ] : … } , $$\nu _T^\tau \left( \cdots \right) = \frac{1} {T}meas\left\{ {\tau \in \left[ {0,T} \right]: \ldots } \right\},$$ where instead of dots we write a condition satisfied by τ. Here meas A denotes the Lebesgue measure of the set A.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-6401-8_5

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DOI: 10.1007/978-94-017-6401-8_5

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