Resumo:In the classical Wiener-Kolmogorov (WK) prediction problem in stochastic processes, one fixes a functional of the process in the “future” and seeks its best predictor in terms of the processes’ “past” (best in the L₂-sense). Our work in speech recognition lead to a variant of this problem: seek the “most predictable” non-trivial functional of the “future” and its best predictor in the “past”. In contrast to the W-K case, the new problem for continuous-time stochastic processes may have no solutions or it may have multiple solutions – depending on the properties of the stochastic process.  In certain cases, the study of this problem is reduced to the study of the spectrum of certain (singular) integral operators on Hardy type spaces and certain spaces of entire functions of finite exponential type. In the former case (Hardy type spaces), we established necessary and sufficient conditions for the operator to be Hilbert-Smith or compact. In the second case (entire functions) our results are weaker (we provide only sufficient conditions for the operator to be compact) and address only the case when the underlying spaces can be imbedded into Sobolev type spaces. In the seminar we will discuss these results and some open questions.

Local: Sala da Pós-Graduação do IM/UFAL (prédio antigo)

Data: 10/07/14 (Quinta-Feira)

Hora: 14:00