Garcia, Jorge Convergence of stochastic integrals and SDE’s associated to approximations of the Gaussian white noise. (English) Zbl 1168.60326 Adv. Appl. Stat. 10, No. 2, 155-177 (2008). Summary: The Gaussian white noise in \(d\) dimensions is approximated in a smooth way by a process \(W_\varepsilon\) which happens to be a semimartingale random measure. Using this approximation, the integral of an associated process to \(W_\varepsilon\) is taken with respect to \(W_\varepsilon\) and also the limit of these integrals is taken as \(\varepsilon\) approaches zero. A Wong and Zakai factor is obtained in the limit. This result is the analogous of a time-smooth approximation of the Brownian motion. Finally, an application to convergence of SDE’s is given, the limit of a sequence of solutions to a stochastic differential equation is taken and the limit is analyzed. MSC: 60F05 Central limit and other weak theorems 60F25 \(L^p\)-limit theorems 60F15 Strong limit theorems 60G51 Processes with independent increments; Lévy processes 60H05 Stochastic integrals 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:stochastic integrals; approximation Gaussian white noise; time and space; convergence; Wong-Zakai correction factor PDFBibTeX XMLCite \textit{J. Garcia}, Adv. Appl. Stat. 10, No. 2, 155--177 (2008; Zbl 1168.60326) Full Text: Link