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The long-memory Gaussian processes presented as the integrals and are considered. The fractional Brownian motion is a particular case when [phi],[psi],h are the power functions. The integrals Vt are transformed into Gaussian martingales. The Girsanov theorem for Bt is stated and the Hellinger...
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A real harmonizable multifractional stable process is defined, its Hölder continuity and localizability are proved. The existence of local time is shown and its regularity is established.
Persistent link: https://www.econbiz.de/10009146666
For a mixed stochastic differential equation driven by independent fractional Brownian motions and Wiener processes, the existence and integrability of the Malliavin derivative of the solution are established. It is also proved that the solution possesses exponential moments.
Persistent link: https://www.econbiz.de/10010709050
We consider the homogeneous stochastic differential equation with unknown parameter to be estimated. We prove that the standard maximum likelihood estimate is strongly consistent under very mild conditions. The conditions for strong consistency of the discretized estimator are established as well.
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Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, <CitationRef CitationID="CR5">1994</CitationRef>) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains...</citationref>
Persistent link: https://www.econbiz.de/10010992888
We study the possibility to control the moments of Wiener integrals of fractional Brownian motion with respect to the Lp- norm of the integrand. It turns out that when the self-similarity index , we can have only an upper inequality, and when we can have only a lower inequality.
Persistent link: https://www.econbiz.de/10005074758
We prove some maximal inequalities for fractional Brownian motions. These extend the Burkholder-Davis-Gundy inequalities for fractional Brownian motions. The methods are based on the integral representations of fractional Brownian motions with respect to a certain Gaussian martingale in terms of...
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