18 papers
Operator Calculus for Population-Based Optimization: A Mean-Field Convergence Theory
Pekka Malo, Lauri Viitasaari, Patrik Nummi +3
Population-based and distributional optimization methods, from evolution strategies and consensus-based optimization to covariance-matrix adaptation and stochastic gradient methods…
Parameter estimation in generalized fractional neuronal models
Pauliina Ilmonen, Milla Laurikkala, Enrica Pirozzi +2
We investigate a generalized stochastic fractional neuronal model combining fractional dynamics with correlated stochastic inputs. The proposed framework is described by a fraction…
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…