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Fluctuation of the transition density for Brownian motion on random recursive Sierpinski gaskets

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  • Hambly, B. M.
  • Kumagai, Takashi

Abstract

We consider a class of random recursive Sierpinski gaskets and examine the short-time asymptotics of the on-diagonal transition density for a natural Brownian motion. In contrast to the case of divergence form operators in or regular fractals we show that there are unbounded fluctuations in the leading order term. Using the resolvent density we are able to explicitly describe the fluctuations in time at typical points in the fractal and, by considering the supremum and infimum of the on-diagonal transition density over all points in the fractal, we can also describe the fluctuations in space.

Suggested Citation

  • Hambly, B. M. & Kumagai, Takashi, 2001. "Fluctuation of the transition density for Brownian motion on random recursive Sierpinski gaskets," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 61-85, March.
    • Handle: RePEc:eee:spapps:v:92:y:2001:i:1:p:61-85
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    Cited by:

    1. Erdem, Rıza & Ekiz, Cesur, 2005. "An interactive two-state model for cell membrane potassium and sodium ion channels in electric fields using the pair approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 417-426.

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