λ-Statistical Convergence of a Sequence of Random Variables in Probability

Sanjoy Ghosal

Department of Mathematics, Kalyani Government Engineering College, Kalyani, Nadia-741235, West Bengal, India.

*Corresponding Author E-mail: sanjoykrghosal@yahoo.co.in

ABSTRACT:

In this paper the ideas of two types of convergences of a sequence of random variables, namely, λ -statistical convergence in probability and λ - statistical convergence in mean of order r are introduced and the interrelationship between them is investigated. Also their certain basic properties are studied.

KEYWORDS: Random variable, probability, λ -statistical convergence in probability, λ -statistical convergence in mean of order r.

Mathematics Subject Classification (2010): 40A05, 40G15, 60B10.

1. INTRODUCTION AND BACKGROUND:

The idea of convergence of a real sequence was extended to statistical convergence by Fast [9] (See also Schoenberg [13]) as follows: If denotes the set of natural numbers and then denotes the cardinality of the set The upper and lower natural densities of the set is defined by

3. REFERENCES:

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Received on 20.01.2014 Accepted on 29.01.2014

Int. J. Tech. 4(1): Jan.-June. 2014; Page 181-185