Variations and estimators for self-similarity parameters via Malliavin calculus
نویسندگان
چکیده
منابع مشابه
Variations and estimators for selfsimilarity parameters via Malliavin calculus
Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for a specific non-Gaussian selfsimilar process, the Rosenblatt process. We apply our results to the design of strongly consistent statistical estimators for the selfsimilarity parameter H . Although in the case of the Rosenblatt process our estimator has non-Gaussian asymp...
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A selfsimilar process is a stochastic process such that any part of its trajectory is invariant under time scaling. Selfsimilar processes are of considerable interest in practice in modeling various phenomena, including internet traffic (see e.g. [26]), hydrology (see e.g. [11] ), or economics (see e.g. [10], [25]). In various applications, empirical data also shows strong correlation of observ...
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This paper considers a controlled Itô-Lévy process the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly nonMarkovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explic...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2009
ISSN: 0091-1798
DOI: 10.1214/09-aop459