The sufficient digits of continuous random variables

A general setting for nested subdivisions of a bounded real set into intervals defining the digits X_1,X_2, ... of a random variable X with a probability density function f is considered. Under the weak condition that f is almost everywhere lower semicontinuous, a coupling between X and a non-negative integer-valued random variable N is established so that X_1, ...,X_N have an interpretation as the “sufficient digits”, since the distribution of (X_{N+1},X_{N+2}, ...) conditioned on (X_1, ...,X_N) does not depend on f. The importance of this coupling result and some suggestions and open problems for future research are discussed. Related papers are available on arXiv: arxiv.org/abs/2404.09525, arxiv.org/abs/2307.06685.

Contact person: Mario Beraha mario.beraha@polimi.it