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Reinforced weak convergence of stochastic processes


  • Drmota, Michael
  • Marckert, Jean-François


We consider a sequence of stochastic processes Xn on C[0,1] converging weakly to X and call it polynomially convergent, if EF(Xn)-->EF(X) for continuous functionals F of polynomial growth. We present a sufficient moment conditions on Xn for polynomial convergence and provide several examples, e.g. discrete excursions and depth first path associated to Galton-Watson trees. This concept leads to a new approach to moments of functionals of rooted trees such as height and path length.

Suggested Citation

  • Drmota, Michael & Marckert, Jean-François, 2005. "Reinforced weak convergence of stochastic processes," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 283-294, March.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:3:p:283-294

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    References listed on IDEAS

    1. Dai, Wen & Robinson, John, 2001. "Empirical saddlepoint approximations of the Studentized mean under simple random sampling," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 331-337, June.
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    Cited by:

    1. Vysotsky, Vladislav, 2010. "On the probability that integrated random walks stay positive," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1178-1193, July.


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