Non-linear functionals of the Brownian bridge and some applications |
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Institution: | 1. Université Pierre Mendés-France, Grenoble, France;2. Universidad Central de Venezuela, Caracas, Venezuela;3. Instituto Venezolano de Investigaciones Cientı́ficas and U.C.V., Caracas, Venezuela |
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Abstract: | Let {bF(t),t∈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. |
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