75 citations · 236 across the 75 of their papers we have counts for
8 papers · 1 filter
Vector-valued Generalised Ornstein-Uhlenbeck Processes
Marko Voutilainen, Lauri Viitasaari, Pauliina Ilmonen +2
Generalisations of the Ornstein-Uhlenbeck process defined through Langevin equation such as fractional Ornstein-Uhlenbeck processes, have recently receiv…
Stochastic Differential Equations with Discontinuous Diffusions
Soledad Torres, Lauri Viitasaari
We study one-dimensional stochastic differential equations of form , where is a suitable Hölder continuous driver such as the fractional Brownian motion $B^H…
Oscillating Gaussian Processes
Pauliina Ilmonen, Soledad Torres, Lauri Viitasaari
In this article we introduce and study oscillating Gaussian processes defined by , where are free parameters an…
On the regularity of complex multiplicative chaos
Janne Junnila, Eero Saksman, Lauri Viitasaari
Denote by the Gaussian multiplicative chaos which is defined using a log-correlated Gaussian field on a domain . The case $β\in\mathbb{R}…
Stochastic differential equations with noise perturbations and Wong-Zakai approximation of fractional Brownian motion
Lauri Viitasaari, Caibin Zeng
In this article we study effects that small perturbations in the noise have to the solution of differential equations driven by Hölder continuous functions of order . As…
Prediction Law of Mixed Gaussian Volterra Processes
Tommi Sottinen, Lauri Viitasaari
We study the regular conditional law of mixed Gaussian Volterra processes under the influence of model disturbances. More precisely, we study prediction of Gaussian Volterra proces…
Integration-by-Parts Characterizations of Gaussian Processes
Ehsan Azmoodeh, Tommi Sottinen, Ciprian A. Tudor +1
The Malliavin integration-by-parts formula is a key ingredient to develop stochastic analysis on the Wiener space. In this article we show that a suitable integration-by-parts form…
Gaussian fluctuations for the stochastic heat equation with colored noise
Jingyu Huang, David Nualart, Lauri Viitasaari +1
In this paper, we present a quantitative central limit theorem for the d-dimensional stochastic heat equation driven by a Gaussian multiplicative noise, which is white in time and…