## Compléments aux formules de Tanaka-Rosen.(French)Zbl 0563.60073

Sémin. de probabilités XIX, Univ. Strasbourg 1983/84, Proc., Lect. Notes Math. 1123, 332-349 (1985).
[For the entire collection see Zbl 0549.00007.]
In this article the author considers the intersection local time $$\alpha$$ (y,$$\Gamma)$$ (y$$\in {\mathbb{R}}$$, $$\Gamma \subset {\mathbb{R}}^ n)$$ of Brownian motion with values in $${\mathbb{R}}^ n$$ $$(n=2$$ or 3) issued of zero. J. Rosen [A representation for the intersection local time of Brownian motion in space, Ann. Probab. 13, 145-153 (1985)] obtained a Tanaka-like formula for $$\alpha$$ (y,$$\Gamma)$$ (y$$\neq 0)$$ involving a specific function. The author generalizes this representation of $$\alpha$$ (y,$$\Gamma)$$ to a class of twice differentiable functions, such that the second derivative satisfies a certain integrability condition. This leads to a generalization of the so-called Varadhan-renormalization describing the behaviour of $$\alpha$$ (y,$$\Gamma)$$ as $$y\downarrow 0$$.
Reviewer: M.Dozzi

### MSC:

 60J65 Brownian motion 60J55 Local time and additive functionals

### Keywords:

intersection; local time; Tanaka-like formula

Zbl 0549.00007
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