On a transformation of the wiener process in $ℝ^m$ by a functional of the local time type on a surface

Abstract

A transformation of the Wiener process $ξ_t$ in $ℝ^m$ is considered. This transformation is realized by a multiplicative functional $α_l = u(ξ_l/u(ξ_0)$, where the function $u$ is constructed in a certain way by using a functional of the local time type on a surface. It is proved that this transformation is equivalent to the successive application of an absolutely continuous change of a measure and killing on the surface.