12 papers · 1 filter
Lower path regularity in all dimensions
Michael Hinz, Jonas M. Tölle, Lauri Viitasaari
We prove precise almost sure lower path regularity results for a wide class of stochastic processes in all space dimensions . Examples include Gaussian processes, in parti…
Error analysis for learning fractional stochastic differential equations with applications in neural approximations
Mahdi Dehshiri, Kerlyns Martinez, Lauri Viitasaari
This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify an…
Smoothness of martingale observables and generalized Feynman-Kac formulas
Alex Karrila, Lauri Viitasaari
We prove that, under the Hörmander criterion on an Itô process, all its martingale observables are smooth. As a consequence, we also obtain a generalized Feynman-Kac formula prov…
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…
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…
1D stochastic pressure equation with log-correlated Gaussian coefficients
Benny Avelin, Tuomo Kuusi, Patrik Nummi +3
We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove we…