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ON CONVERGENCE AND REGULARITY OF VECTOR-VALUED PROCESSES INDEXED BY DIRECTED SETS (DEMICONVERGENCE)

Posted on:1985-04-02Degree:Ph.DType:Dissertation
University:The Ohio State UniversityCandidate:FRANGOS, NICHOLAS EFSTRATIOSFull Text:PDF
GTID:1470390017962058Subject:Mathematics
Abstract/Summary:
The object of investigation convergence of vector-valued pramarts and subpramarts indexed by directed sets (X(,t),F(,t), t (ELEM) J), regularity of vector-valued continuous parameter processes (X(,t),F(,t), t (ELEM) (//R)('+)), and convergence and demiconvergence of real and vector-valued block martingales and submartingales (X(,t),F(,t), t (ELEM) J('m)). Some applications of the latter results to differentiation of integrals in (//R)('m) are also given.
Keywords/Search Tags:Vector-valued, Convergence, Elem
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