Étude asymptotique de certains mouvements browniens complexes avec drift. (French) Zbl 0579.60077
We consider a process in the plane solution of the stochastic differential equation:
\[
dX_ t=dB_ t+b(X_ t)dt
\]
where B denotes a two-dimensional Brownian motion and the function \(b:R^ 2\to R^ 2\) satisfies some integrability conditions which ensure that the process X is recurrent. Limit theorems are proved for the winding numbers of B around several points of the plane, which extend J. W. Pitman and M. Yor’s result in the case without drift [Bull. Am. Math. Soc., New Ser. 10, 109-111 (1984; Zbl 0535.60073) and ”Asymptotic laws of planar Brownian motion.” Ann. Probab., to appear]. Some limit theorems are also proved for the hitting times of small disks centered at distinct points of the plane, when the radius goes to 0. Similar results hold for Brownian motion with bounded drift on the sphere \(S^ 2\).
MSC:
| 60J60 | Diffusion processes |
| 60J65 | Brownian motion |
| 60G17 | Sample path properties |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Citations:
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