SOME PROPERTIES OF RANDOM SERIES IN Lp: CONVERGENCE AND REPRESENTATION WITHOUT LOSS OF INFORMATION

JUAN MIGUEL MEDINA; BRUNO CERNUSCHI FRÍAS

Buenos Aires, Argentina, Agosto 2008

Congreso; IV Congreso Internacional de Matemática Aplicada a la Ingeniería y Enseñanza de la Matemática en la Ingeniería”, INMAT’2008, Agosto 2008, CD-ROM; 2008

Facultad de Ingeniería, UBA

This paper studies some properties of random series in the Lebesgue spaces Lp, where the coefficients are random variables, and the functions constitute a basis of a closed subspace. We are concerned with some pointwise convergence properties, in particular when the functions constitute an lp stable sequence. On the other hand as these series may come from the expansion of a process in a given basis we study the problem of representing a random process without loss of information. These series resembles the Classical Karhunen-Loeve expansion of a L2 process.