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Absolutely continuous states of exit measures for super-Brownian motions with branching restricted to a hyperplane

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Abstract

The exit measures of super-Brownian motions with branching mechanism\(\psi (z) = z^\alpha ,1< \alpha \leqslant 2\) from a bounded smooth domain D in ℝd+1 are known to be absolutely continuous with respect to the surface area on ϑD if\(d< \frac{2}{{a - 1}}\) whereas in the case\(d > 1 + \frac{2}{{a - 1}}\) they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely continuous states for alld≥1.

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References

  1. Dawson, D. A., Fleischmann, K., Super-Brownian motion in higher dimensions with absolutely continuous measure states,J. Theo. Prob., 1995, 8: 179.

    Article  MATH  MathSciNet  Google Scholar 

  2. Dynkin, E. B., Strperprocesses and partial differential equations,Ann. Proh., 1993, 21: 1185.

    Article  MATH  MathSciNet  Google Scholar 

  3. Abraham, R., Le Gall, J-F.. Sur la measure de sortie du super mouvement Brownien, Preprint, 1993.

  4. Sheu, Y-C., On states of exit measures for superdiffusions,Ann. Prob., 1996, 24: 268.

    Article  MATH  MathSciNet  Google Scholar 

  5. Dynkin, E. B., Branching particle systems and superprocesses,Ann. Prob., 1991, 19: 1157,

    Article  MATH  MathSciNet  Google Scholar 

  6. Dunford, N., Schwartz, J. T.,Linear Operator. Part I:General Theory, New York: Interscience, 1958.

    Google Scholar 

  7. Dawson, D. A., Fleischmann, K., Diffusion and reaction caused by point catalysts,SIAM J. Appl. Math., 1992, 52: 163.

    Article  MATH  MathSciNet  Google Scholar 

  8. Dawson, D. A., Fleischmann, K., A super-Brownian motion with a single point catalyst,Stoch. Proc. Appl., 1994, 49: 3.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Departrnt-nt of Mathematics, Nankai University, 300071, Tianjin, China

    Yanxia Ren & Yongjin Wang

Authors
  1. Yanxia Ren
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  2. Yongjin Wang
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Project supported by the National Natural Science Foundation of China (Grant No. 16931063).

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Ren, Y., Wang, Y. Absolutely continuous states of exit measures for super-Brownian motions with branching restricted to a hyperplane. Sci. China Ser. A-Math. 41, 582–594 (1998). https://doi.org/10.1007/BF02876228

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  • DOI: https://doi.org/10.1007/BF02876228

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