14:15
If a distribution, say F, has all moments finite, then either F is unique (M-determinate) in the sense that F is the only distribution with these moments, or F is non-unique (M-indeterminate). In the latter case we suggest a method for constructing a Stieltjes class consisting of infinitely many distributions different from F and all having the same moments as F. We present some shocking examples involving distributions such as N, LogN, Exp and explain what and why. We analyse conditions which are sufficient for F to be M-determinate or M-indeterminate. Then we deal with recent problems from the following areas:
(A) Non-linear (Box-Cox) transformations of random data.
(B) Distributional properties of functionals of stochastic processes.
(C) Random sums of random variables.
If time permits, some open questions will be outlined. The talk will be addressed to colleagues, including doctoral and master students, working or having interests in the area of probability/stochastic processes/statistics and their applications.