Online Mini-Course "Distributions and Moments: Determinacy, Limit Theorems, Inference"
From November 23 to November 27 Jordan Stoyanov (Honorary Professor at Bulgarian Academy of Sciences, Sofia, Bulgaria; Visiting Professor at Shandong University, China) delivered an online course «Distributions and Moments: Determinacy, Limit Theorems, Inference»
1) distributions, moments, bounds, problem of moments, determinacy (M-det), indeterminacy (M-indet), normal distribution, Chebyshev-Markov CLT, Cramer’s condition (m.g.f.), lognormal distribution;
2) shape of distributions, empirical moments, general picture, Stieltjes classes for M-indet distributions, index of dissimilarity, distributional equations, characterizations via moments;
3) checkable conditions, Carleman criterion for determinacy, Krein criterion for indeterminacy, Hardy’s condition, rate of growth of the moments, Pedersen’s condition, functional transformations of random data (Box-Cox), converse conditions, Lin’s condition;
4) Frechet–Shohat limit theorem via convergence of the moments, limit theorem via cumulants (semi-invariants), multivariate distributions, random sums of random variables, random products;
5) inference problems, identifiability of stochastic models, moments in stochastic financial models and actuarial sciences, moments for option pricing, moment properties of stochastic processes, challenging open questions, feedback from participants.