Asymptotic behaviour of a Brownian motion on exterior domains

Probability Theory and Related Fields

Volumn 116, Issue 3, 2000, Pages 303-316

  Collet, Pierre ^a   Martínez, Servet ^b   San Martín, Jaime ^b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

Bessel functions; Brownian motion; Harmonic functions; Heat kernel

Indexed keywords

EID: 0040794523     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050251     Document Type: Article

References (18)

1. Ancona A. Régularité d'Accès des Bouts et Frontière de Martin d'un Domaine Euclidien. J. Math. pures et appl. 63, 215-260 (1984)
2. Ancona A. Théorie du Potentiel sur les Graphes et les Variétés. Ecole d'été de probabilités de Saint Flour XVIII, LNM 1427, Springer Verlag, NY, (1990)
3. n. Ark. für Math. 18, 53-72 (1980)
4. ème Ed., (1969)
5. Bañuelos, R. and Davis, B.: Heat Kernel, Eigenfunctions and Conditioned Brownian Motion in Planar Domains. J. Funct. Anal. 84, 188-200 (1989)
6. Chung K.L. Lectures from Markov Processes to Brownian Motion. Springer Verlag, (1982)
7. Chung, K.L. and Zhao, Z.: From Brownian Motion to Schrödinger's Equation. Springer Verlag, (1995)
8. Carslaw, H.S. and Jaeger, J.C.: Conduction of Heat in Solids. Oxford Science Publ., 2nd Edition, (1959)
9. Collet, P., Martínez, S. and San Martín, J.: Asymptotic Laws for One-Dimensional Diffusions conditioned to Nonabsorption. Ann. of Probability 23, 1300-1314 (1995)
10. Collet, P., Martínez, S. and San Martín, J.: Ratio Limit Theorems for a Brownian Motion Killed at the Boundary of a Benedicks Domain. To appear in Ann. Prob.
11. Doob J.L. Classical Potential Theory and Its Probabilistic Counterpart. Springer Verlag, (1984)
12. Gradshteyn, I.S. and Ryzhik, I.W.: Table of Integrals Series and Products. Academic Press, New York London, (1965)
13. Ioffe, D. and Pinsky, R.: Positive Harmonic Functions Vanishing on the Boundary for the Laplacian in Unbounded Horn-Shaped Domains. Trans. of the AMS 342, 773-791 (1994)
14. Knight F. Essentials of Brownian Motion and Diffusion. Math. Surveys and Monographs 18 AMS, (1981)
15. Mandl P. Spectral Theory of Semi-Groups connected with Diffusions Processes and its Applications. Czech. Math. J. 11, 558-569 (1961)
16. Pinsky R. The Lifetimes of Conditioned Diffusion Processes. Ann. Inst. H. Poincaré 26, 87-99 (1990)
17. Port, S. and Stone, C.: Brownian Motion and Classical Potential Theory. Academic Press, New York London, (1978)
18. Trudinger N. Pointwise Estimates and Quasilinear Parabolic Equations. Comm. Pure Appl. Math. 21, 205-226 (1968)