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On generalized local time for the process of brownian motion
Authors:V. V. Bakun
Abstract:
We prove that the functionals 
$$delta _Gamma  (B_t ) and frac{{partial ^k }}{{partial x_1^k ...partial x_d^{k_d } }}delta _Gamma  (B_t ), k_1  + ... + k_d   =  k > 1,$$
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 
$$(delta _Gamma  ,varphi ) : =  intlimits_Gamma  {varphi (x} )lambda (dx),$$
where ι(·) is a surface measure on Γ.
Keywords:
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