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Least squares estimator of fractional Ornstein Uhlenbeck processes with periodic mean
Salwa Bajja, Khalifa Es-Sebaiy, Lauri Viitasaari
We first study the drift parameter estimation of the fractional Ornstein-Uhlenbeck process (fOU) with periodic mean for every . More precisely, we extend the consi…
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian--fractional Brownian model
Ehsan Azmoodeh, Tommi Sottinen, Lauri Viitasaari
We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is,…
Representation of stationary and stationary increment processes via Langevin equation and self-similar processes
Lauri Viitasaari
Let be a standard Brownian motion. It is well-known that the Langevin equation defines a stationary process called Ornstein-Uhlenbeck process. Furt…
A general approach to small deviation via concentration of measures
Ehsan Azmoodeh, Lauri Viitasaari
We provide a general approach to obtain upper bounds for small deviations in different norms, namely the supremum and - Hölder norms. The larg…
Adapted integral representations of random variables
Georgiy Shevchenko, Lauri Viitasaari
We study integral representations of random variables with respect to general Hölder continuous processes and with respect to two particular cases; fractional Brownian motion and m…
Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes
Ehsan Azmoodeh, Tommi Sottinen, Lauri Viitasaari +1
The continuity of Gaussian processes is extensively studied topic and it culminates in the Talagrand's notion of majorizing measures that gives complicated necessary and sufficient…