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News

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»

Program of the course:

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.