Hybrid Switching Diffusions

Yin, George; Zhu, Chao

doi:10.1007/978-1-4419-1105-6

Cited by 373 publications

(113 citation statements)

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“…We refer the readers to monographs [1,2] on this field for the detailed introduction. As the states of parameters of SDEs can be changed according to some Markov processes, SDEs with Markovian switching are powerful tools to describe systems which encounter abrupt changes in the structure [?…”

Section: Introduction Intromentioning

confidence: 99%

Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

Qiu

Liu

et al. 2016

Statistics & Probability Letters

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Feedback control based on discrete-time state observation for stochastic differential equations with Markovian switching was initialled by Mao (2013). In practice, various effects could cause some time delay in the control function. Therefore, the time delay is taken into account for the discrete-time state observation in this paper and the mean-square exponential stability of the controlled system IS investigated.This paper is devoted as a continuous research to Mao (2013).

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Section: Introduction Intromentioning

confidence: 99%

Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

Qiu

Liu

et al. 2016

Statistics & Probability Letters

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“…To this end, we first observe the "nonzero" property, which asserts that almost all sample paths of all solutions to (2.3) starting from a nonzero initial condition will never reach the origin with probability one. This phenomenon was first established for diffusion processes in Khasminskii (2012) and later extended to regime-switching diffusions in Mao and Yuan (2006), Yin and Zhu (2010) under the usual Lipschitz and linear growth conditions. For processes with Lévy type jumps, additional assumptions are needed to handle the jumps to obtain the "nonzero" property.…”

Section: Introductionmentioning

confidence: 83%

“…For example, as demonstrated in Barone-Adesi and Whaley (1987), the volatility and the expected rate of return of an asset are markedly different in the bull and bear markets. Regime-switching diffusion with Lévy type jumps naturally captures these inherent features of these systems: the Lévy jumps are well-known to incorporate both small and big jumps (Applebaum (2009), Cont and Tankov (2004)) while the regime switching mechanisms provide the qualitative changes of the environment (Mao and Yuan (2006), Yin and Zhu (2010)). In other words, regime-switching diffusion with Lévy jumps provides a uniform and realistic yet mathematically tractable platform in modeling a wide range of applications.…”

Section: Introductionmentioning

confidence: 99%

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

Chao¹,

Wang²,

Zhu³

et al. 2017

SIAM J. Control Optim.

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This work is devoted to almost sure and moment exponential stability of regimeswitching 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 pth moment exponential stabilities are presented. Several examples are provided for illustration.

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“…The first component is usually called the level, while the second one is called the phase. If S is discrete these processes are typically called quasi-birth-and-death processes (see [29,33]), while if S is a continuous real interval, they are called switching diffusion processes (see [31,43]). They key point to study spectral methods of these processes will be the theory of matrix-valued orthogonal polynomials.…”

Section: Introductionmentioning

confidence: 99%

Some bivariate stochastic models arising from group representation theory

Iglesia

Román

2018

Stochastic Processes and their Applications

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Abstract. The aim of this paper is to study some continuous-time bivariate Markov processes arising from group representation theory. The first component (level) can be either discrete (quasi-birth-and-death processes) or continuous (switching diffusion processes), while the second component (phase) will always be discrete and finite. The infinitesimal operators of these processes will be now matrix-valued (either a block tridiagonal matrix or a matrix-valued secondorder differential operator). The matrix-valued spherical functions associated to the compact symmetric pair (SU(2) × SU(2), diag SU(2)) will be eigenfunctions of these infinitesimal operators, so we can perform spectral analysis and study directly some probabilistic aspects of these processes. Among the models we study there will be rational extensions of the one-server queue and Wright-Fisher models involving only mutation effects.

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Hybrid Switching Diffusions

Cited by 373 publications

References 0 publications

Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

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

Some bivariate stochastic models arising from group representation theory

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