4 papers
Walk-on-Cubes Monte Carlo Simulation for nonisotropic fractional Laplace, Helmholtz, and Yukawa equations
Antti Rasila, Tommi Sottinen, Yaotong Yuan
We study the nonisotropic fractional analogs of Laplace, Helmholtz and Yukawa equations. We provide a Duffin correspondence for the Yukawa equation and a Feynman--Kac reconstructio…
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…
On optimal prediction of missing functional data with memory
Pauliina Ilmonen, Nourhan Shafik, Tommi Sottinen +2
This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transfor…