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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 9, Fasc. 1,
pages 95 - 114
 

TIGHTNESS CRITERIA FOR RANDOM MEASURES WITH APPLICATION TO THE PRINCIPLE OF CONDITIONING IN HILBERT SPACES

Adam Jakubowski

Abstract: Suppose that (m ) n is a sequence of random probability measures on a real and separable Hilbert space such that, for each n (- N, m n is a pointwisely convergent convolution of some sequence (m | k (- N) nk of random measures. The sequence (m ) n is said to be shift- tight if one can find random vectors (A ) n such that the ”centered” sequence (m * d ) n - An is tight.

It is proved that for a shift-tight sequence (m ) n there exists a ”progressively measurable” centering which changes (m ) n into a tight sequence.

As an application, Principle of Conditioning and Martingale Central Limit Theorem in a Hilbert space are proved.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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