64 citations · 320 across the 79 of their papers we have counts for
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Boundary non-crossing probabilities for fractional Brownian motion with trend
Enkelejd Hashorva, Yuliya Mishura, Oleg Seleznjev
In this paper we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non…
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…
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…
Standard maximum likelihood drift parameter estimator in the homogeneous diffusion model is always strongly consistent
Yuliya Mishura
We consider the homogeneous stochastic differential equation with unknown parameter to be estimated. We prove that the standard maximum likelihood estimate is strongly consistent u…
Asymptotic behavior of mixed power variations and statistical estimation in mixed models
Marco Dozzi, Yuliya Mishura, Georgiy Shevchenko
We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These…