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Some convergence properties of the sum of Gaussian functionals

Wałachowska A.

Demonstratio Mathematica

2016

Vol. 49, nr 4

453--462

In the paper, some aspects of the convergence of series of dependent Gaussian sequences problem are solved. The necessary and sufficient conditions for the convergence of series of centered dependent indicators are obtained. Some strong convergence results for weighted sums of Gaussian functionals are discussed.

On multivalued amarts

Dudek D., Zięba W.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 1

93-99

In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L^1-bounded B- valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym property [6]. In this paper we solve the problem of a.s. convergence of multivalued amarts by giving a topological characterization.