Some Random Series in $L^p (\mu)$: Convergence and representation without loss of information

JUAN MIGUEL MEDINA; BRUNO CERNUSCHI FRÍAS

Novosibirsk, Rusia

Conferencia; International Conference. Differential Equations, Function Spaces, Approximation Theory; 2008

Instituto Sobolev, Academia de Ciencias de la Federación Rusa

This paper studies some properties of random series of the form P1i=1 aifi in general Lebesgue spaces Lp(X,, µ),with µ -finite, 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 aP1i=1 aifi in general Lebesgue spaces Lp(X,, µ),with µ -finite, 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 aLp(X,, µ),with µ -finite, 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 afi’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 afi’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.2 process.