White Noise Solution for Nonlinear Stochastic Systems: In memory of A.V. Balakrishnan. Issue 18 (2016)

• Record Type: Journal Article
• Authors: Cacace, Filippo; Conte, Francesco; Germani, Alfredo; Palombo, Giovanni
• Is Part Of: IFAC-PapersOnLine. Volume 49:Issue 18(2016)
• Page Start: 327
• Page End: 332
• Publication Date: 2016
• Subjects: White Noise Theory -- Nonlinear Systems -- Nonlinear Stochastic Modeling; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2016.10.186
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper proposes an alternative theory to the Ito calculus due to Balakrishnan: the white noise theory in Hilbert spaces. The proposed approach extends Blakrishnan's theory to a new class of nonlinear systems. The method uses the theory of differential geometry to devise a suitable map which transforms the starting system in an equivalent one; then the techniques of white noise theory is applied to this equivalent system. Finally, by means of the inverse map, the existence of a white noise solution for the starting system is proved.