85 citations · 361 across the 34 of their papers we have counts for
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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…
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…
Stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index
Yuliya Mishura, Georgiy Shevchenko
We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficie…