A Characteristic Martingale Related to the Counting Process of Records

Raúl Gouet (), F. Javier López () and Gerardo Sanz ()
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Raúl Gouet: Universidad de Chile
F. Javier López: Universidad de Zaragoza
Gerardo Sanz: Universidad de Zaragoza

Journal of Theoretical Probability, 2007, vol. 20, issue 3, 443-455

Abstract: Abstract Let (X n ) be a sequence of nonnegative, integrable, independent and identically distributed random variables, with common distribution function F. We consider the problem of finding all distribution functions F such that N n −cM n is a discrete time martingale, where N n is the counting process of upper records, M n =max {X 1,…,X n } is the process of partial maxima and c is a positive constant. We solve the problem by explicitly giving the solution with finite support and using this for constructing the solution for the general case by a limiting process. We show that the set of solutions can be parameterized by their support and the mass at the leftmost point of the support.

Keywords: Characterization of distributions; Martingales; Records (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0065-2

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