Yuliya Mishura

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For a mixed stochastic differential equation involving standard Brownian motion and an almost surely Hölder continuous process Z with Hölder exponent γ > 1/2, we establish a new result on its unique solvability. We also establish an estimate for difference of solutions to such equations with different processes Z and deduce a corresponding limit theorem. As(More)
We adapt the general conditions of the weak convergence for the sequence of processes with discrete time to the diffusion process towards the weak convergence for the discrete-time models of a financial market to the continuous-time diffusion model. These results generalize a classical scheme of the weak convergence for discrete-time markets to the(More)
The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a γ-Hölder continuous process with γ > 1/2 (e.g. a fractional Brownian motion with Hurst parameter greater than 1/2). It is shown that its solution depends continuously on the coefficients and the initial data. Two applications of this result are(More)
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