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Non-linear functionals of the Brownian bridge and some applications

Author

Listed:
  • Berzin-Joseph, Corinne
  • León, José R.
  • Ortega, Joaquín

Abstract

Let {bF(t),t[set membership, variant][0,1]} be an F-Brownian bridge process. We study the asymptotic behaviour of non-linear functionals of regularizations by convolution of this process and apply these results to the estimation of the variance of a non-homogeneous diffusion and to the convergence of the number of crossings of a level by the regularized process to a modification of the local time of the Brownian bridge as the regularization parameter goes to 0.

Suggested Citation

  • Berzin-Joseph, Corinne & León, José R. & Ortega, Joaquín, 2001. "Non-linear functionals of the Brownian bridge and some applications," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 11-30, March.
  • Handle: RePEc:eee:spapps:v:92:y:2001:i:1:p:11-30
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    References listed on IDEAS

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    1. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
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