Moment analysis of probability distributions

We deal with the classical moment problem for probability distributions, continuous or discrete, one-dimensional or multidimensional, coming from random variables or stochastic processes. In this talk the emphasis will be on some recent progress in the moment analysis of distributions. Specific topics which will be discussed are:

• Comments on the classical Carleman condition and the Krein condition.
• New Hardy’s criterion for uniqueness. Multidimensional moment problem.
• Nonlinear transformations of random data and their moment (in)determinacy.
• Moment determinacy of distributions of stochastic processes defined by SDEs.

There will be results, hints for their proof, examples and counterexamples, and also open questions and conjectures.