85 citations · 361 across the 34 of their papers we have counts for
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Integrability of solutions to mixed stochastic differential equations
Georgiy Shevchenko
We prove that the standard conditions that provide unique solvability of a mixed stochastic differential equations also guarantee that its solution possesses finite moments. We als…
Asymptotic Properties of Drift Parameter Estimator Based on Discrete Observations of Stochastic Differential Equation Driven by Fractional Brownian Motion
Yuliya Mishura, Kostiantyn Ral'chenko, Oleg Seleznev +1
We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on d…
Local times for multifractional square Gaussian processes
Georgiy Shevchenko
We consider multifractional process given by double Ito--Wiener integrals, which generalize the multifractional Rosenblatt process. We prove that this process is continuous and has…
On the distribution of local times and integral functionals of a homogeneous diffusion process
Mykola Perestyuk, Yuliya Mishura, Georgiy Shevchenko
In this article we study a homogeneous transient diffusion process . We combine the theories of differential equations and of stochastic processes to obtain new results for homo…
Mixed stochastic delay differential equations
Georgiy Shevchenko
We consider a stochastic delay differential equation driven by a Holder continuous process and a Wiener process. Under fairly general assumptions on its coefficients, we prove that…
Malliavin regularity of solutions to mixed stochastic differential equations
Georgiy Shevchenko, Taras Shalaiko
For a mixed stochastic differential driven by independent fractional Brownian motions and Wiener processes, the existence and integrability of the Malliavin derivative of its solut…