On the moment (in)determinacy of probability distributions

The main discussion will be on heavy tailed probability distributions, one-dimensional or multi-dimensional, with finite all moments. Either such a distribution is uniquely determined by its moment sequence (M-determinate), or it is nonunique (M-indeterminate). Our goal is to describe the current state of art in this area. New results will be reported and some open questions outlined. The talk is based on recent joint works with GD Lin (Taiwan) and C Kleiber (Basel).