Summary
We say that the discD(α)⊂R 2, of radius α, located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzεD(α) there exists a 0≦t≦T such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those α's (α≧0) is studied for which,D(α) isp-covered inT.
References
Knight, F.B.: Essentials of Brownian motion and diffusion. Providence, R.I.: Am Math. Soc. 103 (1981)
Révész, P.: Random walk in random and non-random environments Singapore: World Scientific 1990
Révész, P.: Clusters of a random walk on the plane. Ann. Probab. (to appear) (1992)
Révész, P.: Clusters of a random walk on the plane II. (Manuscript)
Spitzer, F.: Some theorems concerning 2-dimensional Brownian motion. Ann. Math. Soc.87, 187–197 (1958)
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Révész, P. Black holes on the plane drawn by a Wiener process. Probab. Th. Rel. Fields 93, 21–37 (1992). https://doi.org/10.1007/BF01195386
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DOI: https://doi.org/10.1007/BF01195386
Mathematics Subject Classifications (1991)
- 60F15
- 60J65