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Far East Journal of Theoretical Statistics

be an exchangeable sequence of r.v.’s defined on a probability space

We assume that

and prove a Kolmogorov’s type inequality for this sequence. Using the inequality we give an alternative proof of the Strong Law of Large Numbers for such a sequence. An immediate consequence is the well-known Strong Law of Large Numbers for a sequence of independent and identically distributed r.v.’s, such that

In the process of proving the above results, we also prove (basic) properties of exchangeable r.v.’s. All these results are proved in a unified martingale approach.

Far East Journal of Theoretical Statistics
Volume 26, Issue 2, Pages 193 - 206 (November 2008)

KOLMOGOROV’S INEQUALITY FOR EXCHANGEABLE R.V.’S
Tryfon Daras (Greece)

Abstract:
Let

be an exchangeable sequence of r.v.’s defined on a probability space

We assume that

and prove a Kolmogorov’s type inequality for this sequence. Using the inequality we give an alternative proof of the Strong Law of Large Numbers for such a sequence. An immediate consequence is the well-known Strong Law of Large Numbers for a sequence of independent and identically distributed r.v.’s, such that

In the process of proving the above results, we also prove (basic) properties of exchangeable r.v.’s. All these results are proved in a unified martingale approach.

Keywords and phrases: exchangeable sequences, symmetric measures, Kolmogorov’s inequality, martingales, strong law of large numbers.

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P-ISSN: 0972-0863

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