| 概要 | We deal with distributions, continuous or discrete, with finite all moments. Recall that there are distributions which are uniquely determined by their moments, e.g. normal, exponential, beta, binomial, Poisson, etc. However, there are many distributions which are non-unique in terms of the moments, e.g. Log-normal, Log-exponential, cube of normal, etc.
We present criteria for uniqueness and for non-uniqueness of a distribution in terms of its moments. This includes a couple of classical results but the emphasis will be on some new very recent developments. Some unexpected, curious and not well-known facts will be given and explained.
We pay special attention to the moment determinacy of the distributions of Ito stochastic intergrals and the solutions of Ito SDEs.
If time permits some open questions will be outlined.
The talk is dedicated to the memory of Prof. Kiyosi Ito. |