75 citations · 236 across the 75 of their papers we have counts for
10 papers · 1 filter
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,…
Stochastic Analysis of Gaussian Processes via Fredholm Representation
Tommi Sottinen, Lauri Viitasaari
We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm represent…
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…
Aspects of Stochastic Integration with Respect to Processes of Unbounded p-variation
Zhe Chen, Lauri Viitasaari
This paper deals with stochastic integrals of form in a case where the function has discontinuities, and hence the process is usually of unbounded…
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…
Integral representation with adapted continuous integrand with respect to fractional Brownian motion
Georgiy Shevchenko, Lauri Viitasaari
We show that if a random variable is a final value of an adapted Holder continuous process, then it can be represented as a stochastic integral with respect to fractional Brownian…
Multidimensional Breeden-Litzenberger representation for state price densities and static hedging
Jarno Talponen, Lauri Viitasaari
In this article, we consider European options of type depending on several underlying assets. We study how such options can be valued in terms of si…
Pathwise stochastic integrals and Itô formula for multidimensional Gaussian processes
Zhe Chen, Lauri Viitasaari
In this article we study existence of pathwise stochastic integrals with respect to a general class of -dimensional Gaussian processes and a wide class of adapted integrands. Mo…