Stochastic Delay Logistic Model under Regime Switching

Asymptotic properties and simulations of a stochastic logistic model under regime switching

Taking bothwhite noise and colored environmental noise into account, a general stochastic logistic model under regime switching is proposed and studied. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence and global attractivity are established. The critical number between weak persistence and extinction is obtained. Moreover, some simulatio...

Time delay model for the stochastic volatility with regime switching

Sufficient and Necessary Conditions of Stochastic Permanence and Extinction for Stochastic Logistic Populations under Regime Switching

In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the soluti...

Stochastic Functional Differential Equation under Regime Switching

We discuss stochastic functional differential equation under regime switching dx t f xt, r t , t dt q r t x t dW1 t σ r t |x t |βx t dW2 t . We obtain unique global solution of this system without the linear growth condition; furthermore, we prove its asymptotic ultimate boundedness. Using the ergodic property of the Markov chain, we give the sufficient condition of almost surely exponentially ...

Markov Regime Switching Stochastic Volatility

This is a project on modeling time-varying volatility of S&P 500 weely return for the years 1990 to 2012 using Bayesian methods. First, MCMC on the log-stochastic volatility (SV) model is implemented with simulation results analyzed. Second, I generalize the SV model to encompass regime-switching properties with the markov switching log-stochastic volatility (MSSV) model, under which, high-vola...