6 citations · 9 across the 8 of their papers we have counts for
13 papers · 1 filter
Analytical and computational problems related to fractional Gaussian noise
Yuliya Mishura, Kostiantyn Ralchenko, René L. Schilling
We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection, in partic…
On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity
Yuliya Mishura, Kostiantyn Ralchenko, Mounir Zili
We investigate a stochastic partial differential equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a…
Stochastic differential equations driven by additive Volterra-Lévy and Volterra-Gaussian noises
Giulia Di Nunno, Yuliya Mishura, Kostiantyn Ralchenko
We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by Lévy noise. For this purpose, we study in detail smoothnes…
Two methods of estimation of the drift parameters of the Cox-Ingersoll-Ross process: continuous observations
Olena Dehtiar, Yuliya Mishura, Kostiantyn Ralchenko
We consider a stochastic differential equation of the form , where , and are positive constants. The solution corresponds to the…
Maximum likelihood estimation in the non-ergodic fractional Vasicek model
Stanislav Lohvinenko, Kostiantyn Ralchenko
We investigate the fractional Vasicek model described by the stochastic differential equation , , driven by the fractional Brownian motion $B^…
Fractional stochastic heat equation with piecewise constant coefficients
Yuliya Mishura, Kostiantyn Ralchenko, Mounir Zili +1
We introduce a fractional stochastic heat equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infin…