Sommario
La topologia della hypo-convergenza per funzioni semicontinue superiormente consente di trattare come funzioni aleatorie i processi stocastici a realizzazioni semicontinue. La corrispondenza tra misure di probabilità e pre-misure semicontinue superiormente insieme con l’equivalenza tra convergenza debole di misure di probabilità e hypo-convergenza delle corrispondenti pre-misure delinea un contesto topologico maneggevole per trattare processi stocastici le cui realizzazioni sono misure di probabilità. Qui viene esaminato l’aspetto della convergenza quasi certa con particolare riferimento ai problemi asintotici posti dallo studio dei processi empirici.
Summary
The hypo-topology for uppersemicontinuous functions allows to deal with stochastic processes with uppersemicontinuous realizations as random functions. The one-to-one correspondence between probability measures and semi-continuous pre-measures together with the equivalence between weak convergence of probability measures and hypo-convergence of the corresponding pre-measures delineates an handble topological context to deal with measures valued stochastic processes. Almost sure convergence is examined here with special attention devoted to the asymptotic questions posed by empirical processes.
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Bibliografia
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(Conferenza tenuta il 1o guigno 1987)
Lavoro eseguito nell’ambito del progetto MPI 60% Metodologie delle Decisioni Statistiche.
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Salinetti, G. Funzioni aleatorie semicontinue e misure aleatorie. Seminario Mat. e. Fis. di Milano 57, 465–482 (1987). https://doi.org/10.1007/BF02925066
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DOI: https://doi.org/10.1007/BF02925066