Non-linear functionals of the Brownian bridge and some applications

Corinne Berzin-Joseph, José R. León and Joaquín Ortega

Stochastic Processes and their Applications, 2001, vol. 92, issue 1, 11-30

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.

Keywords: Non-linear; functionals; Brownian; bridge; Regularization; by; convolution; Crossings; Local; time; Non-homogeneous; diffusion (search for similar items in EconPapers)
Date: 2001
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