38 citations · 55 across the 8 of their papers we have counts for
7 papers
Stochastic wave equation in a plane driven by spatial stable noise
Larysa Pryhara, Georgiy Shevchenko
The main object of this paper is the planar wave equation \[\bigg(\frac{\partial^2}{\partial t^2}-a^2\varDelta\bigg)U(x,t)=f(x,t),\quad t\ge0, x\in \mathbb {R}^2,\] with random sou…
Convergence of solutions of mixed stochastic delay differential equations with applications
Yuliya Mishura, Taras Shalaiko, Georgiy Shevchenko
The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a -Hölder continuous process with (e.g. a fractional Brown…
Existence of density for solutions of mixed stochastic equations
Taras Shalaiko, Georgiy Shevchenko
We consider a mixed stochastic differential equation driven by independent multidimensional Wiener process and fractional Bro…
Adapted integral representations of random variables
Georgiy Shevchenko, Lauri Viitasaari
We study integral representations of random variables with respect to general Hölder continuous processes and with respect to two particular cases; fractional Brownian motion and m…
Integral representation with adapted continuous integrand with respect to fractional Brownian motion
Georgiy Shevchenko, Lauri Viitasaari
We show that if a random variable is a final value of an adapted Holder continuous process, then it can be represented as a stochastic integral with respect to fractional Brownian…
Mixed fractional stochastic differential equations with jumps
Georgiy Shevchenko
In this paper, we consider a stochastic differential equation driven by a fractional Brownian motion (fBm) and a Wiener process and having jumps. We prove that this equation has a…