On Non-parametric Estimation of the Lévy Kernel of Markov ProcessesReport as inadecuate



 On Non-parametric Estimation of the Lévy Kernel of Markov Processes


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We consider a recurrent Markov process which is an It\^o semi-martingale. The L\evy kernel describes the law of its jumps. Based on observations X0,X{\Delta},

.,Xn{\Delta}, we construct an estimator for the L\evy kernels density. We prove its consistency as n{\Delta}-\infty and {\Delta}-0 and a central limit theorem. In the positive recurrent case, our estimator is asymptotically normal; in the null recurrent case, it is asymptotically mixed normal. Our estimators rate of convergence equals the non-parametric minimax rate of smooth density estimation. The asymptotic bias and variance are analogous to those of the classical Nadaraya-Watson estimator for conditional densities. Asymptotic confidence intervals are provided.



Author: Florian A. J. Ueltzhöfer

Source: https://archive.org/







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