38 citations · 61 across the 10 of their papers we have counts for
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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…
One-to-one correspondences between discrete multivariate stationary, self-similar and stationary increment fields
Marko Voutilainen
In this article, we consider three important classes of -variate fields indexed by the set of dimensional integers, namely stationary, stationary increment and self-similar…
On Lamperti transformation and characterisations of discrete random fields
Marko Voutilainen, Lauri Viitasaari, Pauliina Ilmonen
In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections betwee…
On generalized ARCH model with stationary liquidity
Pauliina Ilmonen, Soledad Torres, Ciprian Tudor +2
We study a generalized ARCH model with liquidity given by a general stationary process. We provide minimal assumptions that ensure the existence and uniqueness of the stationary so…
Note on AR(1)-characterisation of stationary processes and model fitting
Marko Voutilainen, Lauri Viitasaari, Pauliina Ilmonen
It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that,…