Papers by chengcheng ling
Stochastics and Dynamics, 2022
We provide a rather general perfection result for crude local semi-flows taking values in a Polis... more We provide a rather general perfection result for crude local semi-flows taking values in a Polish space showing that a crude semi-flow has a modification which is a (perfect) local semi-flow which is invariant under a suitable metric dynamical system. Such a (local) semi-flow induces a (local) random dynamical system (RDS). Then we show that this result can be applied to several classes of stochastic differential equations driven by semimartingales with stationary increments such as equations with locally monotone coefficients and equations with singular drift. For these examples it was previously unknown whether they generate a (local) RDS or not.
Cornell University - arXiv, Oct 4, 2021
A. We consider a generic and explicit tamed Euler-Maruyama scheme for multidimensional time-inhom... more A. We consider a generic and explicit tamed Euler-Maruyama scheme for multidimensional time-inhomogeneous stochastic di erential equations with multiplicative Brownian noise. The di usive coe cient is uniformly elliptic, Hölder continuous and weakly di erentiable in the spatial variables while the drift satis es the strict Ladyzhenskaya-Prodi-Serrin condition, as considered by Krylov and Röckner (2005). In the discrete scheme, the drift is tamed by replacing it by an approximation. A strong rate of convergence of the scheme is provided in terms of the approximation error of the drift in a suitable and possibly very weak topology. A few examples of approximating drifts are discussed in detail. The parameters of the approximating drifts can vary and-under suitable conditions-be ne-tuned to achieve the standard 1/2-strong convergence rate with a logarithmic factor. The result is then applied to provide numerical solutions for stochastic transport equations with singular vector elds satisfying the aforementioned condition.
Cornell University - arXiv, Oct 9, 2019
In this paper, we prove the existence and uniqueness of maximally defined strong solutions to SDE... more In this paper, we prove the existence and uniqueness of maximally defined strong solutions to SDEs driven by multiplicative noise on general space-time domains Q ⊂ R + × R d , which have continuous paths on the one-point compactification Q ∪ ∂ of Q where ∂ / ∈ Q and Q ∪ ∂ is equipped with the Alexandrov topology. If the SDE is of gradient type (see (2.5) below) we prove that under suitable Lyapunov type conditions the life time of the solution is infinite and its distribution has sub-Gaussian tails. This generalizes earlier work [7] by Krylov and one of the authors to the case where the noise is multiplicative.
Ling C. Stochastic differential equations with singular drifts and multiplicative noises. Bielefe... more Ling C. Stochastic differential equations with singular drifts and multiplicative noises. Bielefeld: Universität Bielefeld; 2020
Potential Analysis, 2020
By studying parabolic equations in mixed-norm spaces, we prove the existence and uniqueness of st... more By studying parabolic equations in mixed-norm spaces, we prove the existence and uniqueness of strong solutions to stochastic differential equations driven by Brownian motion with coefficients in spaces with mixed-norm, which extends Krylov and Rockner's result in [11] and Zhang's result in [18].
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Papers by chengcheng ling