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

Yor, Marc

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

Citations:

Zbl 0549.00007