Archive for the ‘Probability Theory’ Category

## A useful identity in convergence of random series

July 23, 2012
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Let be independent and let Then for any

The identity can be used to prove the following results:

1) P. Levy: Let be independent and let . If exists in probability, then it also exists almost surely.

2) Let be i.i.d. and If in probability, then in probability.

Categories: Probability Theory