All Outputs (4)

Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces (2021)
Journal Article
Feng, C., & Li, L. (2022). Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces. Advances in operator theory, 7, Article 5. https://doi.org/10.1007/s43036-021-00170-1

Saint Raymond asked whether continuously differentiable maps with isolated critical points are necessarily open in infinite dimensional (Hilbert) spaces. We answer this question negatively by constructing counterexamples in various settings including... Read More about Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces.

Ergodicity of Sublinear Markovian Semigroups (2021)
Journal Article
Feng, C., & Zhao, H. (2021). Ergodicity of Sublinear Markovian Semigroups. SIAM Journal on Mathematical Analysis, 53(5), 5646-5681. https://doi.org/10.1137/20m1356518

In this paper, we study the ergodicity of invariant sublinear expectation of sublinear Markovian semigroup. For this, we first develop an ergodic theory of an expectation-preserving map on a sublinear expectation space. Ergodicity is defined as any i... Read More about Ergodicity of Sublinear Markovian Semigroups.

Ergodic Numerical Approximation to Periodic Measures of Stochastic Differential Equations (2021)
Journal Article
Feng, C., Liu, Y., & Zhao, H. (2021). Ergodic Numerical Approximation to Periodic Measures of Stochastic Differential Equations. Journal of Computational and Applied Mathematics, 398, Article 113701. https://doi.org/10.1016/j.cam.2021.113701

In this paper, we consider numerical approximation to periodic measure of a time periodic stochastic differential equations (SDEs) under weakly dissipative condition. For this we first study the existence of the periodic measure ρt and the large time... Read More about Ergodic Numerical Approximation to Periodic Measures of Stochastic Differential Equations.

Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations (2021)
Journal Article
Feng, C., Qu, B., & Zhao, H. (2021). Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations. Journal of Differential Equations, 286, 119-163. https://doi.org/10.1016/j.jde.2021.03.022

In this paper, we define random quasi-periodic paths for random dynamical systems and quasi-periodic measures for Markovian semigroups. We give a sufficient condition for the existence and uniqueness of random quasi-periodic paths and quasi-periodic... Read More about Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations.