A Superprocess Involving Both Branching and Coalescing.
Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
- Published Version
We consider a superprocess with coalescing Brownian spatial motion. We first point out a dual relationship between two systems of coalescing Brownian motions. In consequence we can express the Laplace functionals for the superprocess in terms of coalescing Brownian motions, which allows us to obtain some explicit results. We also point out several connections between such a superprocess and the Arratia flow. A more general model is discussed at the end of this paper.
References:R. Arratia, Coalescing Brownian motions on the line, Ph.D. thesis, University of Wisconsin, Madison 1979.
R. W. R. Darling, Isotropic stochastic flows: a survey, Diffusion Processes and Related Problems in Analysis
(M. Pinsky and M. Wihstutz, eds.) 2 75–94. Birkh¨auser, Boston, 1992.
D. A. Dawson, Z. H. Li, H. Wang, Superprocesses with dependent spatial motion and general branching densities, Elect. J. Probab. 6 (2001) 25, 1–33.
D. A. Dawson, Z. H. Li, Construction of immigration superprocesses with dependent spatial motion from
one–dimensional excursions, Probab. Theory Related Fields, 127 (1) (2003) 37–61.
D. A. Dawson, Z. H. Li, X. Zhou, Rescaled limit of a superprocess with dependent spatial motion, J. Theo. Probab. 17 (3) (2004) 673–692.
A. M. Etheridge, An Introduction to Superprocesses, University Lecture Series Vol. 20, Amer. Math. Soc. 2000.
S. N. Ethier, T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986.
 J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin, 1987.
O. Kallenberg, Random Measures, Academic Press, New York, 1976.
Y. Le Jan, O. Raimond, Flows, coalescence and noise, Ann. Probab. 32 (2) (2005) 1247–1315.
Z. Ma, K. Xiang, Superprocesses of stochastic flows, Ann. Probab. 29 (1) (2001) 317–343.
E. Perkins, Dawson-Watanabe Superprocesses and Measure-valued Diffusions, Lectures on probability theory and statistics (Saint-Flour, 1999), 125–329, Lecture Notes in Math., 1781, Springer, Berlin, 2002.
D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991.
G. Skoulakis, R. J. Adler, Superprocesses over a stochastic flow, Ann. Appl. Probab. 11 (2) (2002) 488–543.
F. Soucaliuc, B. T´oth, W.Werner, Reflection and coalescence between independent one-dimensional Brownian
paths, Ann. Inst. H. Poincar´e Probab. Statist. 36 (4) (2000) 509–545.
B. T´oth, W. Werner, The True self–repelling motion, Probab. Theory Related Fields, 111 (3) (1997) 375–452.
R. Tribe, The behavior of superprocesses near extinction, Ann. Probab. 20 (1) (1992) 286–311.
J. Xiong, X. Zhou, On the duality between coalescing Brownian motions, Canad. J. Math. 57 (1) (2005) 204–224.
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