PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 77(91), pp. 7–19 (2005) 

STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY GENERALIZED POSITIVE NOISEMichael Oberguggenberger and Danijela RajterCiricInstitut für Technische Mathematik, Geometrie und Bauinformatik, Innsbruck, Austria and Institut za matematiku i informatiku, Prirodnomatematicki fakultet, Novi Sad, Serbia and MontenegroAbstract: We consider linear SDEs with the generalized positive noise process standing for the noisy term. Under certain conditions, the solution, a Colombeau generalized stochastic process, is proved to exist. Due to the blowingup of the variance of the solution, we introduce a "new" positive noise process, a renormalization of the usual one. When we consider the same equation but now with the renormalized positive noise, we obtain a solution in the space of Colombeau generalized stochastic processes with both, the first and the second moment, converging to a finite limit. Classification (MSC2000): 46F30; 60G20, 60H10 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 7 Nov 2005. This page was last modified: 11 May 2006.
© 2005 Mathematical Institute of the Serbian Academy of Science and Arts
