A superprocess involving both branching and coalescing

Xiaowen Zhou

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 5, page 599-618
  • ISSN: 0246-0203

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Zhou, Xiaowen. "A superprocess involving both branching and coalescing." Annales de l'I.H.P. Probabilités et statistiques 43.5 (2007): 599-618. <http://eudml.org/doc/77947>.

@article{Zhou2007,
author = {Zhou, Xiaowen},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {coalescing simple random walk; coalescing Brownian motion; duality; superprocess with coalescing Brownian spatial motion; arratia flow; Laplace functional; Feller's branching diffusion; Bessel process},
language = {eng},
number = {5},
pages = {599-618},
publisher = {Elsevier},
title = {A superprocess involving both branching and coalescing},
url = {http://eudml.org/doc/77947},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Zhou, Xiaowen
TI - A superprocess involving both branching and coalescing
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2007
PB - Elsevier
VL - 43
IS - 5
SP - 599
EP - 618
LA - eng
KW - coalescing simple random walk; coalescing Brownian motion; duality; superprocess with coalescing Brownian spatial motion; arratia flow; Laplace functional; Feller's branching diffusion; Bessel process
UR - http://eudml.org/doc/77947
ER -

References

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  1. [1] R. Arratia, Coalescing Brownian motions on the line, Ph.D. thesis, University of Wisconsin, Madison, 1979. 
  2. [2] R.W.R. Darling, Isotropic stochastic flows: a survey, in: Pinsky M., Wihstutz M. (Eds.), Diffusion Processes and Related Problems in Analysis, vol. 2, Birkhäuser, Boston, 1992, pp. 75-94. Zbl0751.60058MR1187986
  3. [3] D.A. Dawson, Z.H. Li, Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions, Probab. Theory Related Fields127 (1) (2003) 37-61. Zbl1038.60082MR2006230
  4. [4] D.A. Dawson, Z.H. Li, H. Wang, Superprocesses with dependent spatial motion and general branching densities, Electron. J. Probab.6 (25) (2001) 1-33. Zbl1008.60093MR1873302
  5. [5] D.A. Dawson, Z.H. Li, X. Zhou, Superprocesses with coalescing Brownian spatial motion as large scale limits, J. Theoret. Probab.17 (3) (2004) 673-692. Zbl1067.60085MR2091555
  6. [6] A.M. Etheridge, An Introduction to Superprocesses, University Lecture Series, vol. 20, Amer. Math. Soc., 2000. Zbl0971.60053MR1779100
  7. [7] S.N. Ethier, T.G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986. Zbl0592.60049MR838085
  8. [8] J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin, 1987. Zbl0635.60021MR959133
  9. [9] O. Kallenberg, Random Measures, Academic Press, New York, 1976. Zbl0345.60032MR431373
  10. [10] Y. Le Jan, O. Raimond, Flows, coalescence and noise, Ann. Probab.32 (2) (2005) 1247-1315. Zbl1065.60066MR2060298
  11. [11] Z. Ma, K. Xiang, Superprocesses of stochastic flows, Ann. Probab.29 (1) (2001) 317-343. Zbl1015.60063MR1825152
  12. [12] E. Perkins, Dawson–Watanabe superprocesses and measure-valued diffusions, in: Lectures on Probability Theory and Statistics, Saint-Flour, 1999, Lecture Notes in Math., vol. 1781, Springer, Berlin, 2002, pp. 125-329. Zbl1020.60075
  13. [13] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991. Zbl0731.60002MR1083357
  14. [14] G. Skoulakis, R.J. Adler, Superprocesses over a stochastic flow, Ann. Appl. Probab.11 (2) (2002) 488-543. Zbl1018.60052MR1843056
  15. [15] F. Soucaliuc, B. Tóth, W. Werner, Reflection and coalescence between independent one-dimensional Brownian paths, Ann. Inst. H. Poincaré Probab. Statist.36 (4) (2000) 509-545. Zbl0968.60072MR1785393
  16. [16] B. Tóth, W. Werner, The True self-repelling motion, Probab. Theory Related Fields111 (3) (1997) 375-452. Zbl0912.60056MR1640799
  17. [17] R. Tribe, The behavior of superprocesses near extinction, Ann. Probab.20 (1) (1992) 286-311. Zbl0749.60046MR1143421
  18. [18] J. Xiong, X. Zhou, On the duality between coalescing Brownian motions, Canad. J. Math.57 (1) (2005) 204-224. Zbl1063.60118MR2113855

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