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Relation among Some Convergence of a Sequences of Random Variables

Wei Xia

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Abstract

In this paper we discuss the relation between almost sure convergence and convergence in probability,and the relation between complete convergence and almost sure convergence.A condition is given under which the convergence in probability of a consequence of random variables can grantee almost sure convergence, and another condition is given under which the almost sure convergence can grantee complete convergence.Hence we obtain completely the relation among some convergence of a sequences of random variables.

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What this paper is about

In this paper we discuss the relation between almost sure convergence and convergence in probability,and the relation between complete convergence and almost sure convergence.A condition is given under which the convergence in probability of a consequence of random variables can grantee almost sure convergence, and another condition is given under which the almost sure convergence can grantee complete convergence.Hence we obtain completely the relation among some convergence of a sequences of random variables.

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Available abstract

In this paper we discuss the relation between almost sure convergence and convergence in probability,and the relation between complete convergence and almost sure convergence.A condition is given under which the convergence in probability of a consequence of random variables can grantee almost sure convergence, and another condition is given under which the almost sure convergence can grantee complete convergence.Hence we obtain completely the relation among some convergence of a sequences of random variables.

Key concepts: Convergence (economics), Convergence of random variables, Relation (database), Convergence tests, Proofs of convergence of random variables, Modes of convergence (annotated index), Mathematics, Compact convergence

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