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Uniform convergence in some limit theorems for multiple particle systems

Author

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  • Giné, Evarist
  • Wellner, Jon A.

Abstract

For n particles diffusing throughout R (or Rd), let [eta]n,t(A), A [epsilon] B, t [greater-or-equal, slanted]0, be the random measure that counts the number of particles in A at time t. It is shown that for some basic models (Brownian particles with or without branching and diffusion with a simple interaction) the processes {([eta]n,t(ø) - E[eta]n,t(ø))/[radical sign]n:t [epsilon] [0,M], ø [epsilon] C[alpha]L(R)}, n [epsilon] N, converge in law uniformly in (t, ø). Previous results consider only convergence in law uniform in t but not in ø. The methods used are from empirical process theory.

Suggested Citation

  • Giné, Evarist & Wellner, Jon A., 1997. "Uniform convergence in some limit theorems for multiple particle systems," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 47-72, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:47-72
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    References listed on IDEAS

    as
    1. Arcones, Miguel A., 1994. "The central limit theorem for U-processes indexed by Hölder's functions," Statistics & Probability Letters, Elsevier, vol. 20(1), pages 57-62, May.
    2. van der Vaart, Aad, 1994. "Bracketing smooth functions," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 93-105, August.
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