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Fluctuations for annihilations of Brownian spheres

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  • Penrose, Mathew D.

Abstract

As a model for a diffusion-limited chemical reaction, we consider a large number N of spheres, of small radius rN, which perform independent Brownian motions in Euclidean space and annihilate one another on contact. We consider the point process of annihilations, and show that according to the limiting behavior of rN, this point process may converge weakly, either to a Poisson process or (after re-normalization) to white noise.

Suggested Citation

  • Penrose, Mathew D., 1994. "Fluctuations for annihilations of Brownian spheres," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 167-189, June.
    • Handle: RePEc:eee:spapps:v:51:y:1994:i:1:p:167-189
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    Cited by:

    1. Penrose, Mathew D., 1995. "Generalised two-sample U-statistics and a two-species reaction-diffusion model," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 57-64, January.

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