All Outputs (22)

Existence of geometric ergodic periodic measures of stochastic differential equations (2023)
Journal Article

Periodic measures are the time-periodic counterpart to invariant measures for dynamical systems and can be used to characterise the long-term periodic behaviour of stochastic systems. This paper gives sufficient conditions for the existence, uniquene... Read More about Existence of geometric ergodic periodic measures of stochastic differential equations.

Periodic measures and Wasserstein distance for analysing periodicity of time series datasets (2023)
Journal Article

In this article, we establish the probability foundation of the periodic measure approach in analysing periodicity of a dataset. It is based on recent work of random periodic processes. While random periodic paths provide a pathwise model for time se... Read More about Periodic measures and Wasserstein distance for analysing periodicity of time series datasets.

Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces (2021)
Journal Article

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

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

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

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.

Ergodicity of invariant capacities (2020)
Journal Article

Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance (2020)
Journal Article

In this paper, we derive a parabolic partial differential equation for the expected exit time of non-autonomous time-periodic non-degenerate stochastic differential equations. This establishes a Feynman–Kac duality between expected exit time of time-... Read More about Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance.

A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations (2020)
Journal Article

This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system generated... Read More about A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations.

Random periodic processes, periodic measures and ergodicity (2020)
Journal Article

Ergodicity of random dynamical systems with a periodic measure is obtained on a Polish space. In the Markovian case, the idea of Poincaré sections is introduced. It is proved that if the periodic measure is PS-ergodic, then it is ergodic. Moreover, i... Read More about Random periodic processes, periodic measures and ergodicity.

Quasi-linear PDEs and forward–backward stochastic differential equations: Weak solutions (2018)
Journal Article

Numerical approximation of random periodic solutions of stochastic differential equations (2017)
Journal Article

Anticipating random periodic solutions—I. SDEs with multiplicative linear noise (2016)
Journal Article

On the Móri-Székely conjectures for the Borel-Cantelli lemma (2013)
Journal Article

Random periodic solutions of SPDEs via integral equations and Wiener–Sobolev compact embedding (2012)
Journal Article

Pathwise random periodic solutions of stochastic differential equations (2011)
Journal Article

Some Inequalities in Functional Analysis, Combinatorics, and Probability Theory (2010)
Journal Article

Local Time Rough Path for Lévy Processes (2010)
Journal Article

On the Borel–Cantelli lemma and its generalization (2009)
Journal Article

Rough path integral of local time (2008)
Journal Article