On generalized local time for the process of brownian motion
Abstract
We prove that the functionals δΓ(Bt)and∂k∂xk1...∂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.Downloads
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.