Some properties of superprocesses under a stochastic flow

Kijung Lee; Carl Mueller; Jie Xiong

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 2, page 477-490
  • ISSN: 0246-0203

Abstract

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For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s Lp-theory for linear SPDE.

How to cite

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Lee, Kijung, Mueller, Carl, and Xiong, Jie. "Some properties of superprocesses under a stochastic flow." Annales de l'I.H.P. Probabilités et statistiques 45.2 (2009): 477-490. <http://eudml.org/doc/78030>.

@article{Lee2009,
abstract = {For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s Lp-theory for linear SPDE.},
author = {Lee, Kijung, Mueller, Carl, Xiong, Jie},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {superprocess; random environment; snake representation; stochastic partial differential equation},
language = {eng},
number = {2},
pages = {477-490},
publisher = {Gauthier-Villars},
title = {Some properties of superprocesses under a stochastic flow},
url = {http://eudml.org/doc/78030},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Lee, Kijung
AU - Mueller, Carl
AU - Xiong, Jie
TI - Some properties of superprocesses under a stochastic flow
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 2
SP - 477
EP - 490
AB - For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s Lp-theory for linear SPDE.
LA - eng
KW - superprocess; random environment; snake representation; stochastic partial differential equation
UR - http://eudml.org/doc/78030
ER -

References

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  11. [11] H. Wang. A class of measure-valued branching diffusions in a random medium. Stochastic Anal. Appl. 16 (1998) 753–786. Zbl0913.60091MR1632574
  12. [12] J. Xiong. A stochastic log-Laplace equation. Ann. Probab. 32 (2004) 2362–2388. Zbl1055.60042MR2078543
  13. [13] J. Xiong. Long-term behavior for superprocesses over a stochastic flow. Electron. Comm. Probab. 9 (2004) 36–52. Zbl1060.60084MR2081458
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