CONTENTSI. Introduction.....................................................................................................................................................................5II. Preliminaries...................................................................................................................................................................7 1. Infinitely divisible probability measures on Banach spaces..........................................................................................7 2. Random measures......................................................................................................................................................9III. Bilinear random integral...............................................................................................................................................11 1. Definition and necessary conditions for the existence of a random integral...............................................................11 2. Topology in the space of M-integrable functions........................................................................................................17 3. Characterization of M-integrable functions.................................................................................................................21 4. Approximation by simple functions and some contraction principles..........................................................................33 5. Stable symmetric random integrals............................................................................................................................42IV. Random integrals of Banach space valued functions with respect to real valued random measures..........................45 1. Immediate corollaries from a general theory of random integrals and examples........................................................45 2. Gaussian and stable random integrals......................................................................................................................51 3. Comparison theorem and some applications.............................................................................................................62References......................................................................................................................................................................70
@book{bwmeta1.element.zamlynska-75305a1b-9ec4-4483-8a24-3cd1946045a1,
author = {Jan Rosi\'nski},
title = {Bilinear random integrals},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1987},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-75305a1b-9ec4-4483-8a24-3cd1946045a1}
}
Jan Rosiński. Bilinear random integrals. GDML_Books (1987), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-75305a1b-9ec4-4483-8a24-3cd1946045a1/