The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Bañuelos, Rodrigo; Smits, Robert G. Brownian motion in cones. Probab. Theory Related Fields 108 (1997), no. 3, 299--319. MR1465162
  • Biane, Philippe. Quelques propriétés du mouvement brownien dans un cone. (French) [Some properties of Brownian motion in a cone] Stochastic Process. Appl. 53 (1994), no. 2, 233--240. MR1302912
  • Biane, Philippe. Permutation model for semi-circular systems and quantum random walks. Pacific J. Math. 171 (1995), no. 2, 373--387. MR1372234
  • Biane, Philippe; Bougerol, Philippe; O'Connell, Neil. Littelmann paths and Brownian paths. Duke Math. J. 130 (2005), no. 1, 127--167. MR2176549
  • Burkholder, D. L. Exit times of Brownian motion, harmonic majorization, and Hardy spaces. Advances in Math. 26 (1977), no. 2, 182--205. MR0474525
  • Chavel, Isaac. Eigenvalues in Riemannian geometry. Including a chapter by Burton Randol. With an appendix by Jozef Dodziuk. Pure and Applied Mathematics, 115. Academic Press, Inc., Orlando, FL, 1984. xiv+362 pp. ISBN: 0-12-170640-0 MR0768584
  • Copson, E. T. Asymptotic expansions. Cambridge Tracts in Mathematics and Mathematical Physics, No. 55 Cambridge University Press, New York 1965 vii+120 pp. MR0168979
  • DeBlassie, R. Dante. Exit times from cones in ${\bf R}^ n$ of Brownian motion. Probab. Theory Related Fields 74 (1987), no. 1, 1--29. MR0863716
  • DeBlassie, R. Dante. Remark on: "Exit times from cones in ${\bf R}^ n$ of Brownian motion'' [Probab. Theory Related Fields 74 (1987), no. 1, 1?29; MR0863716 (88d:60205)]. Probab. Theory Related Fields 79 (1988), no. 1, 95--97. MR0952996
  • Doumerc, Yan; O'Connell, Neil. Exit problems associated with finite reflection groups. Probab. Theory Related Fields 132 (2005), no. 4, 501--538. MR2198200
  • Dyson, Freeman J. A Brownian-motion model for the eigenvalues of a random matrix. J. Mathematical Phys. 3 1962 1191--1198. MR0148397
  • Friedman, Avner. Remarks on the maximum principle for parabolic equations and its applications. Pacific J. Math. 8 1958 201--211. MR0102655
  • Garbit, Rodolphe. Brownian motion conditioned to stay in a cone. J. Math. Kyoto Univ. 49 (2009), no. 3, 573--592. MR2583602
  • Gilbarg, David; Trudinger, Neil S. Elliptic partial differential equations of second order. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 224. Springer-Verlag, Berlin, 1983. xiii+513 pp. ISBN: 3-540-13025-X MR0737190
  • Grabiner, David J. Brownian motion in a Weyl chamber, non-colliding particles, and random matrices. Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), no. 2, 177--204. MR1678525
  • Hunt, G. A. Some theorems concerning Brownian motion. Trans. Amer. Math. Soc. 81 (1956), 294--319. MR0079377
  • Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940
  • Karlin, Samuel; McGregor, James. Coincidence probabilities. Pacific J. Math. 9 1959 1141--1164. MR0114248
  • Kinderlehrer, David; Nirenberg, Louis. Analyticity at the boundary of solutions of nonlinear second-order parabolic equations. Comm. Pure Appl. Math. 31 (1978), no. 3, 283--338. MR0460897
  • König, W.; Schmid, P. Brownian motion in a truncated Weyl chamber. Markov Process. Related Fields 17 (2011), no. 4, 499--522. MR2918119
  • Meyre, Thierry. Étude asymptotique du temps passé par le mouvement brownien dans un cône. (French) [Asymptotic study of the sojourn time of Brownian motion in a cone] Ann. Inst. H. Poincaré Probab. Statist. 27 (1991), no. 1, 107--124. MR1098566
  • Morrey, C. B., Jr.; Nirenberg, L. On the analyticity of the solutions of linear elliptic systems of partial differential equations. Comm. Pure Appl. Math. 10 (1957), 271--290. MR0089334
  • Puchała, Zbigniew; Rolski, Tomasz. The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts. Probab. Theory Related Fields 142 (2008), no. 3-4, 595--617. MR2438702
  • Spitzer, Frank. Some theorems concerning $2$-dimensional Brownian motion. Trans. Amer. Math. Soc. 87 1958 187--197. MR0104296
  • Watson, G. N. A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. vi+804 pp. MR0010746
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.