Variational principles for average exit time moments for diffusions in Euclidean space

Authors:
Kimberly K. J. Kinateder and Patrick McDonald

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2767-2772

MSC (1991):
Primary 60J65, 58G32

DOI:
https://doi.org/10.1090/S0002-9939-99-04843-1

Published electronically:
April 15, 1999

MathSciNet review:
1600101

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Abstract | References | Similar Articles | Additional Information

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

**[AK]**Athreya, K. B. and Kurtz, T. G. (1973),*A generalization of Dynkin's identity*, Ann. of Prob.**1**, 570-579. MR**50:1342****[H]**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****[P2]**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:
https://doi.org/10.1090/S0002-9939-99-04843-1

Keywords:
Diffusions,
exit times,
variational principles

Received by editor(s):
June 2, 1997

Received by editor(s) in revised form:
November 24, 1997

Published electronically:
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

Article copyright:
© Copyright 1999
American Mathematical Society