Differential equations and dynamical systems
Differential equations and dynamical systems
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Hierarchical decision making in stochastic manufacturing systems
Hierarchical decision making in stochastic manufacturing systems
On the Adaptive Control for Jump Parameter Systems viaNonlinear Filtering
SIAM Journal on Control and Optimization
Continuous-time Markov chains and applications: a singular perturbation approach
Continuous-time Markov chains and applications: a singular perturbation approach
Estimation Problems in Hybrid Systems
Estimation Problems in Hybrid Systems
Stock Trading: An Optimal Selling Rule
SIAM Journal on Control and Optimization
Recursive Algorithms for Stock Liquidation: A Stochastic Optimization Approach
SIAM Journal on Optimization
SIAM Journal on Control and Optimization
Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model
SIAM Journal on Control and Optimization
Stabilization and destabilization of hybrid systems of stochastic differential equations
Automatica (Journal of IFAC)
Asymptotic Properties of Hybrid Diffusion Systems
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
On Strong Feller, Recurrence, and Weak Stabilization of Regime-Switching Diffusions
SIAM Journal on Control and Optimization
Numerical methods for controlled regime-switching diffusions and regime-switching jump diffusions
Automatica (Journal of IFAC)
IEEE Transactions on Information Theory
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This work provides a survey on some of the recent progress of switching diffusion systems. In recent years, switching diffusion systems have gained much popularity owing to their flexibility in modeling and their nature to conveniently depict the coexistence of continuous dynamics and discrete events. In this paper, we begin with a number of motivating examples to display a variety of applications that can be covered by switching diffusions. Then we study several important properties of the underlying systems. First weak stability is treated, and then ergodicity is considered, which provides us with a useful tool to replace the time-varying system measures by an ergodic or limit measure. Stability for equilibria is also examined. For the totally degenerated diffusions (i.e., no Gaussian noise case), we are dealing with switched ordinary differential equations. A somewhat surprising discovery is an insight different from the well-know Hartman-Grobman theorem regarding linearization. Numerical approximation for the solution of controlled switching diffusions are also considered.