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Professor Huaizhong Zhao's Outputs (36)

Stochastic differential games with controlled regime-switching (2024)
Journal Article
Ma, C., & Zhao, H. (2024). Stochastic differential games with controlled regime-switching. Computational and Applied Mathematics, 43(4), Article 264. https://doi.org/10.1007/s40314-024-02782-8

In this article, we consider a two-player zero-sum stochastic differential game with regime-switching. Different from the results in existing literature on stochastic differential games with regime-switching, we consider a game between a Markov chain... Read More about Stochastic differential games with controlled regime-switching.

Optimal Control of Probability on A Target Set for Continuous-Time Markov Chains (2023)
Journal Article
Ma, C., & Zhao, H. (online). Optimal Control of Probability on A Target Set for Continuous-Time Markov Chains. IEEE Transactions on Automatic Control, 69(2), 1202-1209. https://doi.org/10.1109/tac.2023.3278789

In this paper, a stochastic optimal control problem is considered for a continuous-time Markov chain taking values in a denumerable state space over a fixed finite horizon. The optimality criterion is the probability that the process remains in a tar... Read More about Optimal Control of Probability on A Target Set for Continuous-Time Markov Chains.

Existence of geometric ergodic periodic measures of stochastic differential equations (2023)
Journal Article
Feng, C., Zhao, H., & Zhong, J. (2023). Existence of geometric ergodic periodic measures of stochastic differential equations. Journal of Differential Equations, 359, 67-106. https://doi.org/10.1016/j.jde.2023.02.022

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
Feng, C., Liu, Y., & Zhao, H. (2023). Periodic measures and Wasserstein distance for analysing periodicity of time series datasets. Communications in Nonlinear Science and Numerical Simulation, 120, Article 107166. https://doi.org/10.1016/j.cnsns.2023.107166

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.

Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations (2022)
Journal Article
Zhang, Q., & Zhao, H. (2022). Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations. Journal of Differential Equations, 331, 1-49. https://doi.org/10.1016/j.jde.2022.05.015

In this paper, we first study the connection between mass-conserving SPDEs on a bounded domain and backward doubly stochastic differential equations, which is a new extension of nonlinear Feynman-Kac formula to mass-conserving SPDEs. Then the infinit... Read More about Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations.

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.

Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance (2020)
Journal Article
Feng, C., Zhao, H., & Zhong, J. (2021). Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance. Physica D: Nonlinear Phenomena, 417, https://doi.org/10.1016/j.physd.2020.132815

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
Feng, C., Qu, B., & Zhao, H. (2020). A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations. Nonlinearity, 33(10), https://doi.org/10.1088/1361-6544/ab9584

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
Feng, C., & Zhao, H. (2020). Random periodic processes, periodic measures and ergodicity. Journal of Differential Equations, 269(9), 7382-7428. https://doi.org/10.1016/j.jde.2020.05.034

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.

Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients (2011)
Journal Article
Zhang, Q., & Zhao, H. (2012). Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients. Journal of Theoretical Probability, 25, 396–423. https://doi.org/10.1007/s10959-011-0350-y

In this paper we develop a new weak convergence and compact embedding method to study the existence and uniqueness of the L2p
ρ (Rd ;R1)×L2ρ(Rd ;Rd ) valued solution of backward stochastic differential equations with p-growth coefficients.
Then we... Read More about Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients.

Numerical approximations to the stationary solutions of stochastic differential equations (2011)
Journal Article
Yevik, A., & Zhao, H. (2011). Numerical approximations to the stationary solutions of stochastic differential equations. SIAM Journal on Numerical Analysis, 49(4), 1397 - 1416. https://doi.org/10.1137/100797886

In this paper, we investigate the possibility of approximating the stationary solution of a stochastic differential equation (SDE). We start with the random dynamical system generated by the SDE with the multiplicative noise. We prove that the pullba... Read More about Numerical approximations to the stationary solutions of stochastic differential equations.

Random periodic solutions of random dynamical systems (2008)
Journal Article
Zheng, Z., & Zhao, H. (2009). Random periodic solutions of random dynamical systems. Journal of Differential Equations, 246(5), 2020-2038. https://doi.org/10.1016/j.jde.2008.10.011

In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a
perfect cocycle on a cylinder using a random invariant set, the Lyapunov exponents and the... Read More about Random periodic solutions of random dynamical systems.