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Non-linear functionals of the Brownian bridge and some applications. (English) Zbl 1047.60082

Summary: Let \(\{b^F (t), t\in [0,1]\}\) be an \(F\)-Brownian bridge process. We study the asymptotic behaviour of nonlinear 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 \(0\).

MSC:

60J65 Brownian motion
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