arXiv subjects
Publications and source records attributed to Remigijus Mikulevičius.
An integro-differential Kolmogorov equation is considered in Hölder-type spaces defined by a scalable Lévy measure. Some properties of those spaces and estimates of the solution are derived using probabilistic representations.
The paper studies the rate of convergence of the weak Euler approximation for Itô diffusion and jump processes with Hölder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in Hölder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.