Conditional and Quantitative Strong Laws of Large Numbers

A tétel rövid nézete
dc.contributor.advisorFazekas, István
dc.contributor.authorMasasila, Nyanga Honda
dc.contributor.departmentInformatikai tudományok doktori iskolahu
dc.contributor.submitterdepInformatikai Kar
dc.date.accessioned2026-04-25T05:28:19Z
dc.date.available2026-04-25T05:28:19Z
dc.date.defended2026
dc.date.issued2026
dc.description.abstractThis dissertation investigates advanced generalizations of the Strong Law of Large Numbers (SLLN) within conditional, multi-indexed, and nonlinear probabilistic frameworks. The first part establishes a general conditional SLLN by proving that conditional Kolmogorov-type maximal inequalities imply conditional Hájek–Rényi inequalities, which in turn yield almost sure convergence of normalized partial sums. The second part develops quantitative SLLNs for double-indexed random variables, deriving explicit probability bounds and convergence rates for pairwise independent and quasi-uncorrelated arrays. The third part extends the theory to conditional sub-additive expectations and capacities, where strong laws are formulated in terms of quasi-sure convergence in non-additive probability spaces. Further results are obtained for φ-sub-Gaussian random variables under sublinear expectations, showing that exponential tail control is sufficient for strong convergence without classical moment assumptions.
dc.format.extent88
dc.identifier.urihttps://hdl.handle.net/2437/406475
dc.language.isoen
dc.subjectStrong law of large numbers
dc.subjectConditional expectation
dc.subjectRate of convergence
dc.subjectSublinear expectation space
dc.subjectSub-Gaussian random variables
dc.subject.disciplineInformatikai tudományokhu
dc.subject.sciencefieldMűszaki tudományokhu
dc.titleConditional and Quantitative Strong Laws of Large Numbers
dc.title.translatedNagy számok feltételes és kvantitatív erős törvényei
dc.typePhD, doktori értekezéshu
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