Some properties of the Itô-Wiener expansion of the solution of a stochastic differential equation and local times (Q429298)

From the author's abstract: We use the formula for the Ito-Wiener expansion of the solution of a stochastic differential equation proven by \textit{B. Kawohl} and \textit{N. Kutev} [Funkc. Ekvacioj, Ser. Int. 43, No. 2, 241--253 (2000; Zbl 1142.35315)] to obtain several results concerning some properties of this expansion. Our main goal is to study the Ito-Wiener expansion of the local time at the fixed point for the solution of the stochastic differential equation in the multidimensional case (when standard local time does not exist even for Brownian motion). We show that under some conditions the renormalized local time exists in the functional space defined by the \(L_{2}\)-norm of the action of some smoothing operator.