Continuability of local weak limits for record values

Abstract

In this paper it is proved that the weak convergence on a compact interval to a continuous, strictly increasing limit function, of the distribution function of a record value, implies weak convergence throughout ℝ.

Keywords:

• record values
• restricted convergence
• weak convergence
• continuation of the convergence

Mathematics Subject Classification :

• Primary: 60F05
• 62E20
• Secondary: 62E15
• 62G30

Acknowledgements

The author would like to thank the Associate Editor Professor Tomasz Rychlik for his kind concern and the anonymous referees for constructive comments and suggestions leading to improvement of the presentation of the paper.