S ep 2 00 7 Self-Similar Stable Processes Arising From High-Density Limits of Occupation Times of Particle Systems ( Self-Similar Stable Processes and Particle Systems )

@inproceedings{BOJDECKI2007SE2,
  title={S ep 2 00 7 Self-Similar Stable Processes Arising From High-Density Limits of Occupation Times of Particle Systems ( Self-Similar Stable Processes and Particle Systems )},
  author={T. BOJDECKI and Luis G. Gorostiza and A. TALARCZYK},
  year={2007}
}
We extend results on time-rescaled occupation time fluctuation limits of the (d, α, β)-branching particle system (0 < α ≤ 2, 0 < β ≤ 1) with Poisson initial condition. The earlier results in the homogeneous case (i.e., with Lebesgue initial intensity measure) were obtained for dimensions d > α/β only, since the particle system becomes locally extinct if d ≤ α/β. In this paper we show that by introducing high density of the initial Poisson configuration, limits are obtained for all dimensions… CONTINUE READING

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