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Variational principles for average exit time moments for diffusions in Euclidean space
Author(s):
Kimberly
K. J.
Kinateder;
Patrick
McDonald
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2767-2772.
MSC (1991):
Primary 60J65, 58G32
Posted:
April 15, 1999
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Abstract:
Let  be a smoothly bounded domain in Euclidean space and let  be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from  of a particle driven by  where the average is taken over all starting points in 
References:
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- Athreya, K. B. and Kurtz, T. G. (1973), A generalization of Dynkin's identity, Ann. of Prob. 1, 570-579. MR 50:1342
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- Ha'sminskii, R. Z. (1960), Probabilistic representation of the solution of some differential equations, Proc. 6th All Union Conf. on Theor. Probability and Math. Statist. (Vilnius 1960) (See Math Rev. 3127 v.32 (1966) pg. 632). MR 32:3127
- [KM1]
- Kinateder, K. K. J. and McDonald, P. (1997), Brownian functionals on hypersurfaces in Euclidean space, Proc. Amer. Math. Soc. 125 6, 1815-1822. MR 97g:60109
- [KMM]
- Kinateder, K. K. J., McDonald, P., and Miller, D. F., Boundary Value Problems and Exit Times for Diffusions in Euclidean Space. Prob. Th. Rel. 111 (1998), pp. 2767-2772.
CMP 99:01 - [P1]
- Pinsky, M., Mean exit times and hitting probabilities of Brownian motion in geodesic balls and tubular neighborhoods, Stochastic Processes - Mathematics and Physics, Lecture Notes in Mathematics, vol. 1158, Springer Verlag, New York, pp. 216-223. MR 87g:58129
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- Polya, G. (1948), Torsional rigidity, principal frequency, electrostatic capacity and symmetrization, Quart. Appl. Math. 6, 267-277. MR 10:206b
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Additional Information:
Kimberly
K. J.
Kinateder
Affiliation:
Department of Mathematics, Wright State University, Dayton, Ohio 45435
Patrick
McDonald
Affiliation:
Department of Mathematics, New College of the University of South Florida, Sarasota, Florida 34243
Email:
pmacdona@virtu.sar.usf.edu
DOI:
10.1090/S0002-9939-99-04843-1
PII:
S 0002-9939(99)04843-1
Keywords:
Diffusions,
exit times,
variational principles
Received by editor(s):
June 2, 1997
Received by editor(s) in revised form:
November 24, 1997
Posted:
April 15, 1999
Additional Notes:
The second author was partially supported by a DSR grant from the University of South Florida.
Communicated by:
Stanley Sawyer
Copyright of article:
Copyright
1999,
American Mathematical Society
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