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Register a new userAsymptotic properties of a stochastic Gilpin-Ayala model under regime switching
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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.
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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.
We study a stochastic SIS epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant set for the system. Then, we find sufficient conditions for a.s. extinction and stochastic permanence, showing also their relation with the stationary probability distribution of the Markov chain that governs the switching. We provide an asymptotic lower bound for the time average of the sample-path solution under the conditions ensuring stochastic permanence. From this bound, we are able to prove the existence of an invariant probability measure if the condition of stochastic permanence holds. Under a different condition, we prove the positive recurrence and the ergodicity of the regime-switching diffusion.
In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold $lambda$ that is used to classify the extinction and permanence of the disease. In particular, $lambda<0$ implies that the disease-free $(K, 0, 0)$ is globally asymptotic stable, i.e., the disease will eventually disappear. If $lambda>0$ the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in cite{HZ1, GLM1, LOK1, SLJJ1, ZJ1}.
In this paper, we investigate the global existence of almost surely positive solution to a stochastic Nicholsons 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 Nicholsons Blowflies Delayed Differential Equations, Appl. Math. Lett. 87 (2019) 20-26.
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model has been successfully used where the volatility is expressed as a stochastic differential equation. In addition, we consider a regime switching model where the stock volatility dynamics depends on an underlying process which is possibly a non-Markov pure jump process. Under this model assumption, we find the locally risk minimizing pricing of European type vanilla options. The price function is shown to satisfy a Heston type PDE.
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