Zhou, Xiaowen (2005) Stepping-Stone Model with Circular Brownian Migration. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
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Abstract
In this paper we consider a stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow and the marginal distribution of this model. We then give a new representation for the stepping-stone model using Arratia flow and circular coalescing Brownian motion. Such a representation enables us to carry out some explicit computation. In particular, we find the Laplace transform for the time when there is only a single type left across the circle.
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Monograph (Technical Report) |
| Authors: | Zhou, Xiaowen |
| Series Name: | Department of Mathematics & Statistics. Technical Report No. 5/05 |
| Corporate Authors: | Concordia University. Department of Mathematics & Statistics |
| Institution: | Concordia University |
| Date: | August 2005 |
| Keywords: | stepping-stone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law |
| ID Code: | 6670 |
| Deposited By: | DIANE MICHAUD |
| Deposited On: | 02 Jun 2010 17:14 |
| Last Modified: | 18 Jan 2018 17:29 |
References:
R. Arratia. Coalescing Brownian motions on the line. PhD thesis, University of Wisconsin, Madison, 1979.P. Donnelly, S.N. Evans, K. Fleischmann, T.G. Kurtz, and X. Zhou. Continuum-sites steppingstone models, coalescing exchangeable partitions, and random trees. Ann. Probab., 28:1063–1110, 2000.
P. Donnelly and T. G. Kurtz. A countable representation of the fleming-viot measure-valued diffusion. Ann. Probab., 24:698–742, 1996.
S.N. Evans. Coalescing markov labeled partitions and continuous sites genetics model with infinitely many types. Ann. Inst. H. Poincar´e Probab., 33:339–358, 1997.
M. Kimura. “stepping-stone” models of population. Technical Report 3, Institute of Genetics, Japan, 1953.
F. B. Knight. Essentials of Brownian Motion and Diffusion. Amer. Math. Soc., Providence, RI, 1981.
T.M. Liggett. Interacting Particle Systems. Springer-Verlag, New York, 1985.
D. Revuz and M. Yor. Continuous Martingales and Brownian motion. Springer-Verlag, Berlin, 1991.
T. Shiga. Stepping stone models in population genetics and population dynamics. Stochastic Processes Phys. Engng. Math. Appl., 42:345–355, 1988.
X. Zhou. A superprocess involving both branching and coalescing. Submitted.
X. Zhou. Clustering behavior of a continuous-sites stepping-stone model with brownian migration. Elect. J. Probab., 8:1–15, 2003.
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