arXiv subjects

Yanling Zhu

Publications and source records attributed to Yanling Zhu.

6 recordsLinked to original sources

arXiv2024

A Markovian regime-switching stochastic SEQIR epidemic model with governmental policy

In this paper, a stochastic SEQIR epidemic model with Markovian regime-switching is proposed and investigated. The governmental policy and implement efficiency are concerned by a generalized incidence function of the susceptible class. We have the existence and uniqueness of the globally positive solution to the stochastic model by using the Lyapunov method. In addition, we study the dynamical behaviors of the disease, and the sufficient conditions for the extinction and persistence in mean are obtained. Finally, numerical simulations are introduced to demonstrate the theoretical results.

math.PR↗

arXiv2019

Dynamics of a mean-reverting stochastic volatility model with regime switching

In this paper, we consider a mean-reverting stochastic volatility equation with regime switching, and present some sufficient conditions for the existence of global positive solution, asymptotic boundedness in pth moment, positive recurrence and existence of stationary distribution of this equation. Some results obtained in this paper extend the ones in literature. Example is given to verify the results by simulation.

math.PR↗

arXiv2019

Stochastic Nicholson's blowflies delay differential equation with regime switching

In this paper, we investigate the global existence of almost surely positive solution to a stochastic Nicholson's blowflies delay differential equation with regime switching, and give the estimation of the path. The results presented in this paper extend some corresponding results in Wang et al. Stochastic Nicholson's Blowflies Delayed Differential Equations, Appl. Math. Lett. 87 (2019) 20-26.

math.PR↗

arXiv2018

Asymptotic properties of a stochastic Gilpin-Ayala model under regime switching

In this paper, a stochastic Gilpin-Ayala population model with regime switching and white noise is considered. All parameters are influenced by stochastic perturbations. The existence of global positive solution, asymptotic stability in probability, $p$th moment exponential stability, extinction, weak persistence, stochastic permanence and stationary distribution of the model are investigated, which generalize some results in the literatures. Moreover, the conditions presented for the stochastic permanence and the existence of stationary distribution improve the previous results.

math.PR↗

arXiv2018

M-estimation in high-dimensional linear model

We mainly study the M-estimation method for the high-dimensional linear regression model, and discuss the properties of M-estimator when the penalty term is the local linear approximation. In fact, M-estimation method is a framework, which covers the methods of the least absolute deviation, the quantile regression, least squares regression and Huber regression. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of numerical simulation, we select the appropriate algorithm to show the good robustness of this method

math.PR↗

arXiv2017

Almost Sure and Moment Exponential Stability of Regime-Switching Jump Diffusions

This work is devoted to almost sure and moment exponential stability of regime-switching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for stabilities for general nonlinear systems; which further helps to derive easily verifiable conditions for linear systems. For one-dimensional linear regime-switching jump diffusions, necessary and sufficient conditions for almost sure and $p$th moment exponential stabilities are presented. Several examples are provided for illustration.

math.PR↗