The exit distribution for iterated Brownian motion in cones

Stochastic Processes and their Applications

Volumn 116, Issue 1, 2006, Pages 36-69

  Bañuelos, Rodrigo ^a   DeBlassie, Dante ^b  

^a PURDUE UNIVERSITY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Exact constants; Harmonic measure; Iterated Brownian motion

Indexed keywords

CONES; HARMONIC ANALYSIS; INFORMATION ANALYSIS; ITERATIVE METHODS;

EXACT CONSTANTS; HARMONIC MEASURES; ITERATED BROWNIAN MOTION;

BROWNIAN MOVEMENT;

EID: 28044442745     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2005.07.003     Document Type: Article

References (28)

1. M. Abramowitz, and I.A. Stegun Handbook of Mathematical Functions 1972 Dover New York
2. H. Allouba Brownian-time process: the PDE connection II and the corresponding Feynman-Kac formula Trans. Amer. Math. Soc. 354 2002 4627 4637
3. H. Allouba, and W. Zheng Brownian-time processes: the PDE connection and the half-derivative generator Ann. Probab. 29 2001 1780 1795
4. R. Bañuelos, T. Carroll, Sharp integrability for Brownian motion in parabola-shaped regions, J. Funct. Anal. 218 (2005) 219-253.
5. R. Bañuelos, R.D. DeBlassie, and R. Smits The first exit time of planar Brownian motion from the interior of a parabola Ann. Prob. 29 2001 882 901
6. R. Bañuelos, and R.G. Smits Brownian motion in cones Probab. Theory Related Fields 108 1997 299 319
7. M. Vandenberg Subexponential behaviour of the Dirichlet heat kernel J. Funct. Anal. 198 2003 28 42
8. K. Burdzy Some path properties of iterated Brownian motion E. Cinlar K.L. Chung M.J. Sharpe Seminar on Stochastic Processes 1993 Birkhäuser Boston 67 87
9. K. Burdzy, and D. Khoshnevisan Brownian motion in a Brownian crack Ann. Appl. Probab. 8 1998 708 748
10. D.L. Burkholder Exit times of Brownian motion, harmonic majorization and Hardy spaces Adv. in Math. 26 1977 182 205
11. I. Chavel Eigenvalues in Riemann Geometry 1984 Academic Press New York
12. E. Csáki, M. Csörgo, A. Földes, and P. Révész The local time of iterated Brownian motion J. Theoret. Probab. 9 1996 717 743
13. R.D. DeBlassie Exit times from cones in R n of Brownian motion Probab. Theory Related Fields 74 1987 1 29
14. R.D. DeBlassie Remark on exit times from cones in R n of Brownian motion Probab. Theory Related Fields 79 1988 95 97
15. R.D. DeBlassie, R. Smits, Brownian motion in twisted domains, Trans. Amer. Math. Soc. 357 (2005) 1245-1274.
16. R.D. DeBlassie, Iterated Brownian motion in an open set, Ann. Appl. Probab. 14 (2004) 1529-1558.
17. M. Essén, and K. Haliste A problem of Burkholder and the existence of harmonic majorants of | x | p in certain domains in R d Ann. Acad. Sci. Fenn. Ser. A. I. Math. 9 1984 107 116
18. D. Gilbarg, and N. Trudinger Elliptic Partial Differential Equations of Second Order second ed. 1983 Springer Berlin
19. I.S. Gradshteyn, and I.M. Ryzhik Table of Integrals, Series and Products 1980 Academic New York
20. K. Haliste Some estimates of harmonic majorants Ann. Acad. Sci. Fenn. Ser. A. I. Math. 9 1984 117 124
21. P. Hsu Brownian exit distribution of a ball Seminar in Stochastic Processes 1986 Birkhäuser Boston 108 116
22. D. Khoshnevisan, and T.M. Lewis Chung's law of the iterated logarithm for iterated Brownian motion Ann. Inst. Henri Poincaré 32 1996 349 359
23. W. Li The first exit time of Brownian motion from an unbounded convex domain Ann. Probab. 31 2003 1078 1096
24. M. Lifshitz, and Z. Shi The first exit time of Brownian motion from parabolic domain Bernoulli 8 2000 745 765
25. R.G. Pinsky Positive Harmonic Functions and Diffusion 1995 Cambridge University Press Cambridge
26. M. Protter, and H. Weinberger Maximum Principles in Differential Equations 1984 Springer New York
27. G.N. Watson A Treatise on the Theory of Bessel Functions second ed. 1922 Cambridge University Press Cambridge
28. Y. Xiao Local times and related properties of multidimensional iterated Brownian motion J. Theoret. Probab. 11 1998 383 408