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Some properties of the Itô-Wiener expansion of the solution of a stochastic differential equation and local times. (English) Zbl 1248.60066
From the author’s abstract: We use the formula for the Ito-Wiener expansion of the solution of a stochastic differential equation proven by B. Kawohl and 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.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J55 Local time and additive functionals
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