Afrika Matematika

, Volume 25, Issue 3, pp 681–692

\(\mathcal{I }\)-statistical convergence of a sequence of random variables in probability

Authors

    • Department of Mathematics, Faculty of ScienceKalyani Government Engineering College
Article

DOI: 10.1007/s13370-013-0142-x

Cite this article as:
Ghosal, S. Afr. Mat. (2014) 25: 681. doi:10.1007/s13370-013-0142-x

Abstract

In this paper we make a new approach to some well known summability methods using ideals and introducing new notions like \(\mathcal{I }\)-statistical convergence of a sequence of random variables in probability, \(\mathcal{I }\)-lacunary statistical convergence of a sequence of random variables in probability and \(\mathcal{I }\)-\(\lambda \)-statistical convergence of a sequence of random variables in probability. Further we investigate their interrelationship and study some of their important properties.

Keywords

Random variable \(\mathcal{I }\)-statistical convergence \(\mathcal{I }\)-lacunary statistical convergence \(\mathcal{I }\)-\(\lambda \)-statistical convergence \([V, \lambda ]\) (\(\mathcal{I }\))-summability

Mathematics Subject Classification (2010)

40Axx 40Cxx 60Fxx 60Gxx

Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2013