SOME PROPERTIES OF RANDOM SERIES IN Lp(µ):

JUAN MIGUEL MEDINA; BRUNO CERNUSCHI FRÍAS

Universidad de Buenos Aires, Buenos Aires, Argentina

Congreso; IV Congreso Internacional de matemática Aplicada a la Ingeniería, InMat 2008; 2008

This paper studies some properties of random series of the form 1Pi=11Pi=1 aifi in the Lebesgue spaces Lp(X,, µ), where the ai’s are random variables, and the fi’s constitute a basis of a closed subspace. We are concerned with some pointwise convergence properties, in particular when the fi’s 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-Lo´eve expansion of a L2 process.ifi in the Lebesgue spaces Lp(X,, µ), where the ai’s are random variables, and the fi’s constitute a basis of a closed subspace. We are concerned with some pointwise convergence properties, in particular when the fi’s 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-Lo´eve expansion of a L2 process.Lp(X,, µ), where the ai’s are random variables, and the fi’s constitute a basis of a closed subspace. We are concerned with some pointwise convergence properties, in particular when the fi’s 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-Lo´eve expansion of a L2 process.fi’s 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-Lo´eve expansion of a L2 process.L2 process.