|
Jordan curves in the level sets of additive Brownian motion
Author(s):
Robert
C.
Dalang;
T.
Mountford
Journal:
Trans. Amer. Math. Soc.
353
(2001),
3531-3545.
MSC (2000):
Primary 60G60;
Secondary 60G15
Posted:
April 24, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
This paper studies the topological and connectivity properties of the level sets of additive Brownian motion. More precisely, for each excursion set of this process from a fixed level, we give an explicit construction of a closed Jordan curve contained in the boundary of this excursion set, and in particular, in the level set of this process.
References:
-
- 1.
- Dalang, R.C. & Mountford, T. Nondifferentiability of curves on the Brownian sheet. Ann. Probab. 24 (1996), 182-195. MR 97e:60129
- 2.
- Dalang, R.C. & Mountford, T. Points of increase of the Brownian sheet. Probab. Th. Rel. Fields 108 (1997), 1-27.MR 2000e:60084
- 3.
- Dalang, R.C. & Mountford, T. Eccentric behaviors of the Brownian sheet along lines. Annals Probab. (2001, to appear).
- 4.
- Dalang, R.C. & Walsh, J.B. Geography of the level sets of the Brownian sheet. Probab. Th. Rel. Fields 96 (1993), 153-176.MR 94k:60055
- 5.
- Dalang, R.C. & Walsh, J.B. The structure of a Brownian bubble. Probab. Th. Rel. Fields 96 (1993), 475-501. MR 94j:60105
- 6.
- Fitzsimmons, P.J. & Salisbury, Th.S. Capacity and energy for multiparameter Markov processes. Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), 325-350. MR 91d:60180
- 7.
- Kendall, W.S. Contours of Brownian processes with several-dimensional times. Z. Wahrsch. Verw. Gebiete 52 (1980), 267-276.MR 83a:60066
- 8.
- Khoshnevisan, D. & Shi, Z. Brownian sheet and capacity. Ann. Probab. 27 (1999), 1135-1159. CMP 2000:06
- 9.
- Mandelbaum, A. Continuous multi-armed bandits and multiparameter processes. Ann. Probab. 15 (1987), 1527-1556.MR 89b:62169
- 10.
- Mountford, T.S. Estimates of the Hausdorff dimension of the boundary of positive Brownian sheet components. In: Sém. de Probab. XXVII, Lect. Notes in Math. 1557, Springer, Berlin (1993), 233-255.MR 96b:60216
- 11.
- Walsh, J.B. Optional increasing paths. In: Processus aléatoires à deux indices (Paris, 1980), Lect. Notes in Math. 863, Springer, Berlin (1981), 172-201. MR 82k:60101
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
60G60,
60G15
Retrieve articles in all Journals with MSC
(2000):
60G60,
60G15
Additional Information:
Robert
C.
Dalang
Affiliation:
Département de Mathématiques, Ecole Polytechnique Fédérale, 1015 Lausanne, Switzerland
Email:
robert.dalang@epfl.ch
T.
Mountford
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90024
Email:
malloy@math.ucla.edu
DOI:
10.1090/S0002-9947-01-02811-2
PII:
S 0002-9947(01)02811-2
Keywords:
Additive Brownian motion,
Brownian sheet,
level set,
Jordan curve
Received by editor(s):
May 11, 2000
Posted:
April 24, 2001
Additional Notes:
The research of the first author is partially supported by the Swiss National Foundation for Scientific Research
The research of the second author is partially supported by NSF grant DMS-9703815 and by the Sloan Foundation
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org