Evans, Steven N. and Zhou, Xiaowen (2004) Balls-In-Boxes Duality for Coalescing Random Walks and Coalescing Brownian Motions. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
Preview |
Text (application/pdf)
293kB8_04_Evans_Zhou.pdf - Published Version |
Abstract
We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends previous work in the literature and we apply it to the study of a system of coalescing Brownian motions with Poisson immigration.
Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
---|---|
Item Type: | Monograph (Technical Report) |
Authors: | Evans, Steven N. and Zhou, Xiaowen |
Series Name: | Department of Mathematics & Statistics. Technical Report No. 8/04 |
Corporate Authors: | Concordia University. Department of Mathematics & Statistics |
Institution: | Concordia University |
Date: | September 2004 |
ID Code: | 6656 |
Deposited By: | DIANE MICHAUD |
Deposited On: | 02 Jun 2010 16:15 |
Last Modified: | 18 Jan 2018 17:29 |
References:
R. Arratia. Coalescing Brownian motions on the line. PhD thesis, University of Wisconsin,Madison, 1979.
M. Abramowitz and L. A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Wiley, New York, 1972.
P. Donnelly, S. N. Evans, F. Fleischmann, T. G. Kurtz, and Z. Zhou. Continuum-sites steppingstone models, coalescing exchangeable partitions, and random trees. Ann. Probab., 28:1063–1110, 2000.
S. N. Ethier and T. G. Kurtz. Markov Processes: Characterization and Convergence. Wiley, New York, 1986.
D. Griffeath. Additive and cancellative interacting particle systems, volume 724 of Lecture Notes in Mathematics. Springer, Berlin, 1979.
R. K. Getoor and M. J. Sharpe. Excursions of Brownian motion and Bessel processes. Z. Wahrsch. Verw. Gebiete, 47(1):83–106, 1979.
T. E. Harris. Coalescing and noncoalescing stochastic flows in R1. Stoch. Proc. Appl., 17:187–210, 1984.
O. Kallenberg. Random Measures. Academic Press, New York, 1976.
A. Lachal. L’int´egrale du mouvement brownien. J. Appl. Prob., 30:17–27, 1993.
M. Lefebvre. First-passage densities of a two-dimensional process. SIAM J. Appl. Math., 49(5):1514–1523, 1989.
T. M. Liggett. Stochastic interacting systems: contact, voter and exclusion processes, volume 324 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1999.
Y. Le Jan and O. Raimond. Integration of Brownian vector fields. Ann. Probab., 30(2):826–873, 2002.
Y. Le Jan and O. Raimond. Flots de noyaux et flots coalescents. C. R. Math. Acad. Sci. Paris, 336(2):181–184, 2003.
F. Soucaliuc, B. T´oth, and W. Werner. Reflection and coalescence between independent onedimensional brownian paths. Ann. Inst. H. Poincar´e Probab., 36:509–545, 2000.
B. Tsirelson. Within and beyond the reach of Brownian innovation. In Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), number Extra Vol. III, pages 311–320 (electronic), 1998.
B. Tsirelson. Scaling limit, noise, stability. In J. Picard, editor, Lectures on probability theory and statistics : Ecole d’été de probabilites de Saint-Flour XXXII-2002, volume 1840, pages 1–106. Springer, Berlin, 2004.
B. T´oth and W. Werner. The true self–repelling motion. Probab. Theory Related Fields, 111:375–452, 1997.
J. Warren. The noise made by a Poisson snake. Electron. J. Probab., 7:no. 21, 21 pp. (electronic), 2002.
J. Xiong and X. Zhou. On the duality between coalescing brownian motions. To appear in Can. J. Math.
X. Zhou. Clustering behavior of continuous-site stepping-stone model with brownian migration. Elec. J. Probab., 8(11):1–15, 2003.
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.
Repository Staff Only: item control page