On generalized local time for the process of brownian motion

Authors

  • V. V. Вакип

Abstract

We prove that the functionals δΓ(Bt)andkxk1...xkddδΓ(Bt),k1+...+kd=k>1, of a d-dimensional Brownian process are Hida distributions, i.e., generalized Wiener functionals. Here, δΓ(·) is a generalization of the δ-function constructed on a bounded closed smooth surface Γ⊂R d , k≥1 and acting on finite continuous functions φ(·) in R d according to the rule (δΓ,φ):=Γφ(x)λ(dx), where ι(·) is a surface measure on Γ.

Published

25.02.2000

Issue

Section

Research articles

How to Cite

Вакип V. V. “On Generalized Local Time for the Process of Brownian Motion”. Ukrains’kyi Matematychnyi Zhurnal, vol. 52, no. 2, Feb. 2000, pp. 157-64, https://umj.imath.kiev.ua/index.php/umj/article/view/4405.