Jordan Stoyanov: Probability Distributions and Their Moment Determinacy
Na Seminarju iz Verjetnosti, statistike in finančne matematike bo 19. marca predaval profesor Jordan Stoyanov. Profesor Stoyanov je doktoriral na Moskovski državni univerzi, kjer je bil njegov mentor profesor Albert Širjajev. Po doktoratu je bil raziskovalec na Bolgarski akademiji znanosti in profesor na Univerzi v Sofiji. Od leta 1999 do nedavne upokojitve pa je deloval na Univerzi v Newcastlu v Veliki Britaniji. Med drugim je avtor večih knjig iz teorije verjetnosti. Najbolj znana med njimi je Counterexamples in Probability, katere tretjo izdajo je leta 2013 izdala založba Dover Publications.
Predavanje na seminarju bo splošno, namenjeno širšemu krogu matematikov. Vabljeni!
Abstract:
The main discussion will be on probability distributions with finite all moments. The distributions come from random variables, random vectors or stochastic processes. There are two possibilities: either such a distribution is uniquely determined by its moment sequence (M-determinate), or it is non-unique (M-indeterminate). After a brief summary of known and widely used classical results (Cramer, Hausdorff, Carleman, Krein,…), we focus our attention on some very recent developments (Stieltjes classes, Hardy’s condition, rate of growth of moments). The moments of distributions and the moment determinacy are essentially involved in studying phenomena which are random and dynamic. This will be illustrated by analyzing popular stochastic financial models.
