75 citations · 236 across the 75 of their papers we have counts for
9 papers · 1 filter
On fractal minimizers and potentials of occupation measures
Michael Hinz, Jonas M. Tölle, Lauri Viitasaari
We consider four prototypes of variational problems and prove the existence of fractal minimizers through the direct method in the calculus of variations. By design these minimizer…
Extended Kalman Filtering on Stiefel Manifolds
Jordi-Lluís Figueras, Aron Persson, Lauri Viitasaari
A generalisation of the extended Kalman filter for Stiefel manifold-valued measurements is presented. We provide simulations on the 2-sphere and the space of orthogonal 4-by-2 matr…
On the Convergence of the Extended Kalman Filter on Stiefel Manifolds when Observing a Constant Particle with Measurement Errors
Jordi-Lluís Figueras, Aron Persson, Lauri Viitasaari
In this paper we first introduce the setting of filtering on Stiefel manifolds. Then, assuming the underlying system process is constant, the convergence of the extended Kalman fil…
Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration
Marko Voutilainen, Pauliina Ilmonen, Lauri Viitasaari
In this article, we characterize continuous stationary fields via generalized Langevin dynamics. This gives natural connections between stationary fields, stationary increment fiel…
Non-parametric estimation of non-linear diffusion coefficient in parabolic SPDEs
Martin Andersson, Benny Avelin, Valentin Garino +2
In this article, we introduce a novel non-parametric predictor, based on conditional expectation, for the unknown diffusion coefficient function in the stochastic partial diffe…
Data driven modeling of multiple interest rates with generalized Vasicek-type models
Pauliina Ilmonen, Milla Laurikkala, Kostiantyn Ralchenko +2
The Vasicek model is a commonly used interest rate model, and there exist many extensions and generalizations of it. However, most generalizations of the model are either univariat…
Tanaka formula for SDEs driven by fractional Brownian motion
Tommi Sottinen, Ercan Sönmez, Lauri Viitasaari
We derive a Tanaka-type formula for the solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (fBm) with Hurst parameter . Whil…
Moment Estimator-Based Extreme Quantile Estimation with Erroneous Observations: Application to Elliptical Extreme Quantile Region Estimation
Jaakko Pere, Pauliina Ilmonen, Lauri Viitasaari
In many application areas of extreme value theory, the variables of interest are not directly observable but instead contain errors. In this article, we quantify the effect of thes…
Cut-off phenomenon and asymptotic mixing for multivariate general linear processes
Gerardo Barrera, Michael A. Högele, Pauliina Ilmonen +1
The small noise cut-off phenomenon in continuous time and space has been studied in the recent literature for the linear and non-linear stable Langevin dynamics with additive Lévy…