On the occupation measure of super-Brownian motion

Jean-Francois Le Gall (Ecole normale superieure de Paris)
Mathieu Merle (UBC Vancouver)

Abstract


We derive the asymptotic behavior of the total occupation measure of the unit ball for super-Brownian motion started from the Dirac measure at a distant point and conditioned to hit the unit ball. In the critical dimension 4, we obtain a limiting exponential distribution.

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Pages: 252-265

Publication Date: October 12, 2006

DOI: 10.1214/ECP.v11-1225

References

  1. D.A. Dawson D.A., I. Iscoe I. and E.A. Perkins. Super-Brownian motion: Path properties and hitting probabilities. Probab. Th. Rel. Fields 83(1989), 135-205. Math. Review 90k:60073
  2. K. Itô and H.P. McKean. Diffusion Processes and their Sample Paths.Springer (1965). Math. Review 199891
  3. T.Y. Lee. Asymptotic results for super-Brownian motions and semilinear differential equations. Ann. Probab.29 (2001), 1047-1060. Math. Review 2002i:60055
  4. J.F. Le Gall. Spatial Branching Processes, Random Snakes and Partial Differential Equations. Lectures in Mathematics ETH Zürich. Birkhäuser (1999). Math. Review 2001g:60211
  5. J.F. Le Gall. The Hausdorff measure of the range of super-Brownian motion. In: Perplexing Problems in Probability. Festschrift in Honor of Harry Kesten.M. Bramson, R. Durrett eds, pp. 285-314. Birkhäuser (1999). Math. Review 2001j:60095
  6. M. Merle. Local behaviour of local times of super-Brownian motion. Ann. Institut H. Poincaré Probab. Stat.42 (2006), 491-520. Math. Review 2242957
  7. E.A. Perkins. Dawson-Watanabe Superprocesses and Measure-Valued Diffusions. Lectures on Probability Theory and Statistics, Ecole d'été de Probabilités de Saint-Flour XXIX. Springer Lecture Notes Math. 1781, pp.125-329 (2002). Math. Review 2003k:60104
  8. S. Sugitani. Some properties for the measure-valued branching diffusion process. J. Math. Soc. Japan41 (1989), 437-462. Math. Review 91a:60223
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