Exponential ergodicity for regime-switching diffusion processes in total variation norm

<p style='text-indent:20px;'>We investigate the long time behavior for a class of regime-switching diffusion processes. Based on direct evaluation of moments and exponential functionals of hitting time of the underlying process, we adopt coupling method to obtain existence and uniqueness of the invariant probability measure and establish explicit exponential bounds for the rate of convergence to the invariant probability measure in total variation norm. In addition, we provide some concrete examples to illustrate our main results which reveal impact of random switching on stochastic stability and convergence rate of the system.</p>

Constrained stochastic LQ control on infinite time horizon with regime switching

This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. To tackle the problem, two new extended stochastic Riccati equations (ESREs) on infinite time horizon are introduced. The existence of the nonnegative solutions, in both standard and singular cases, is proved through a sequence of ESREs on finite time horizon. Based on this result and some approximation techniques, we obtain the optimal state feedback control and optimal value for the stochastic LQ problem explicitly. Finally, we apply these results to solve a lifetime portfolio selection problem of tracking a given wealth level with regime switching and portfolio constraint.

Dynamic Analysis of a Stochastic Rumor Propagation Model with Regime Switching

We study the rumor propagation model with regime switching considering both colored and white noises. Firstly, by constructing suitable Lyapunov functions, the sufficient conditions for ergodic stationary distribution and extinction are obtained. Then we obtain the threshold Rs which guarantees the extinction and the existence of the stationary distribution of the rumor. Finally, numerical simulations are performed to verify our model. The results indicated that there is a unique ergodic stationary distribution when Rs>1. The rumor becomes extinct exponentially with probability one when Rs<1.

The Multi-Compartment SI(RD) Model with Regime Switching: An Application to COVID-19 Pandemic

We study—with existence and unicity results—a variant of the SIR model for an infectious disease incorporating both the possibility of a death outcome—in a short period of time—and a regime switch that can account for the mitigation measures used to control the spreading of the infections, such as a total lockdown. This model is parametrised by three parameters: the basic reproduction number, the mortality rate of the infected, and the duration of the disease. We discuss a particular example of application to Portuguese COVID-19 data in two short periods just after the start of the epidemic in 4 March 2020, with the first two cases dated that day. We propose a simple and effective method for the estimation of the main parameters of the disease, namely, the basic reproduction number and the mortality rate of the infected. We correct these estimated values to take into account the asymptomatic non-diagnosed members of the population. We compare the outcome of the model in the cases of the existence, or not, of a regime switch, and under three different scenarios, with a remarkable agreement between model and data deaths in the case of our basis scenario. In a final short remark, we deal with the existence of symmetries for the proposed model.