64 citations · 320 across the 79 of their papers we have counts for
5 papers · 2 filters
On drift parameter estimation in models with fractional Brownian motion
Yuriy Kozachenko, Alexander Melnikov, Yuliya Mishura
We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum l…
Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions
Yuliya Mishura, Georgiy Shevchenko
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely Hölder continuous process with Hölder exponent , we establish a new…
The rate of convergence of estimate for Hurst index of fractional Brownian motion involved into stochastic differential equation
K. Kubilius, Y. Mishura
We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according…
Rate of convergence of Euler approximations of solution to mixed stochastic differential equation involving Brownian motion and fractional Brownian motion
Yulia Mishura, Georgiy Shevchenko
We consider a mixed stochastic differential equation involving both standard Brownian motion and fractional Brownian motion with Hurst parameter . The mean-square rate of co…
Random variables as pathwise integrals with respect to fractional Brownian motion
Yuliya Mishura, Georgiy Shevchenko, Esko Valkeila
We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand can have any prescribed distribution, moreover, we give both ne…