Poincaré-Type Inequalities for Compact Degenerate Pure Jump Markov Processes

Hodara, Pierre; Papageorgiou, Ioannis

doi:10.3390/math7060518

Cited by 7 publications

(10 citation statements)

References 36 publications

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“…Besides, recall that the Markov model simulates well some stochastic problems in real engineering [26][27][28][29][30][31]. In Model 7, k i (i = 1, 2, 3) represents the feedback profit coefficient, which is also stochastic in a dynamic economic market.…”

Section: Remarkmentioning

confidence: 99%

Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

Rao

2019

Mathematics

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The intrinsic instability of the financial system itself results in chaos and unpredictable economic behavior. To gain the globally asymptotic stability of the equilibrium point with a positive interest rate of the chaotic financial system, pulse control is sometimes very necessary and is employed in this paper to derive the globally exponential stability of financial system. It should be pointed out that the delayed feedback model brings an essential difficulty so that the regional control method has to be adopted. In this paper, the author firstly employs impulsive control, regional control, the Lyapunov function technique, and variational methods to derive the stochastically globally asymptotic stability criterion of the economic balance point with a positive interest rate for a delayed feedback financial system with Markovian jumping and partially unknown transition rates. Besides, the mathematical induction method and the proof by contradiction are applied synthetically to deduce the globally exponential stability of the equilibrium point with a positive interest rate for the impulsive financial system without time-delays. Moreover, numerical examples illustrate that under suitable data conditions on the two main criteria mentioned above, the interest rates are positive decimals when the financial system reaches stability, which means better economic significance.

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Section: Remarkmentioning

confidence: 99%

Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

Rao

2019

Mathematics

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“…Markov systems often occur in various engineering technologies (see, for example, [9][10][11]). Particularly, a Markovian jumping delayed feedback model well reflects the influence of stochastic factors on time delays in the changes of populations, such as weather, temperature, humidity, ventilation status, etc.…”

Section: Introductionmentioning

confidence: 99%

Global Stabilization of a Single-Species Ecosystem with Markovian Jumping under Neumann Boundary Value via Laplacian Semigroup

Rao

Jia-lin²,

Yang

2021

Mathematics

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By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods.

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“…Markov systems often occurred in various engineering technologies (see, e.g. [24][25][26]). Particularly, Markovian jumping delayed feedback model reflects well the influence of stochastic factors on time delays of the changes of populations, such as weather, temperature, humidity, ventilation status, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…For example, freshwater fish do not enter the sea through rivers. Inspired by some ideas or methods of the related literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]30], the author is to investigate the stability of a single-species Markovian jumping ecosystem with diffusion and delayed feedback under Neumann zero boundary value.…”

Section: Introductionmentioning

confidence: 99%