9 citations · 9 across the 5 of their papers we have counts for
5 papers
Consistency of the drift parameter estimator for the discretized fractional Ornstein-Uhlenbeck process with Hurst index
Kestutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko +1
We consider Langevin equation involving fractional Brownian motion with Hurst index . Its solution is the fractional Ornstein-Uhlenbeck process and with unknown dr…
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…
Ruin probability in a risk model with a variable premium intensity and risky investments
Yuliya Mishura, Mykola Perestyuk, Olena Ragulina
We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky ass…
Example of a Gaussian self-similar field with stationary rectangular increments that is not a fractional Brownian sheet
Vitalii Makogin, Yuliya Mishura
We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet. This Gaussian field is an extension of fractional Brownian motion. We prove some p…
Approximation of fractional Brownian motion by martingales
Sergiy Shklyar, Georgiy Shevchenko, Yuliya Mishura +2
We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in…