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

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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.

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Acknowledgment

We are thankful to the referee for his valuable suggestions which has improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kalyani Government Engineering College, Kalyani, Nadia, 741235, West Bengal, India

    Sanjoy Ghosal

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  1. Sanjoy Ghosal
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Correspondence to Sanjoy Ghosal.

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Ghosal, S. \(\mathcal{I }\)-statistical convergence of a sequence of random variables in probability. Afr. Mat. 25, 681–692 (2014). https://doi.org/10.1007/s13370-013-0142-x

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