New regularity of kolmogorov equation and application on approximation of semi-linear spdes with Hölder continuous drifts

Abstract

In this paper, some new results on the the regularity of Kolmogorov equations associated to the infinite dimensional OU-process are obtained. As an application, the average L 2 -error on [0, T ] of exponential integrator scheme for a range of semi-linear stochastic partial differential equations is derived, where the drift term is assumed to be Hölder continuous with respect to the Sobolev norm · β for some appropriate β > 0. In addition, under a stronger condition on the drift, the strong convergence estimate is obtained, which covers the result of the SDEs with Hölder continuous drift.2000 Mathematics Subject Classification. Primary: 60H15, 35R60, 65C30.

Central limit theorem and self-normalized Cramér-type moderate deviation for Euler-Maruyama scheme

“…When g or σ is irregular, there have recently been some works, see Bao, Huang and Yuan [2] for the convergence rate of degenerate SDEs. We refer the reader to Bao and Shao [3], Shao [35] for the EM scheme of path-dependent SDEs and to Bao and Yuan [4] for that of stochastic differential delay equations.…”

Central limit theorem and Self-normalized Cramér-type moderate deviation for Euler-Maruyama Scheme

“…, the constant C T usually tends to ∞ as T → ∞. When g or σ is irregular, there have recently been some works, see Bao et al (2019) for the convergence rate of degenerate SDEs. We refer the reader to Bao and Shao (2018); Shao (2018) for the EM scheme of path-dependent SDEs and to Bao and Yuan (2013) for that of stochastic differential delay equations.…”