85 citations · 361 across the 34 of their papers we have counts for
5 papers · 1 filter
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…
Fractional Brownian motion in a nutshell
Georgiy Shevchenko
This is an extended version of the lecture notes to a mini-course devoted to fractional Brownian motion and delivered to the participants of 7th Jagna International Workshop.
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…