Stochastic Nicholson’s blowflies delay differential equation with regime switching

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 ...

Time delay model for the stochastic volatility with regime switching

Neutral Stochastic Differential Delay Equations with Markovian Switching

Neutral stochastic differential delay equations (NSDDEs) have recently been studied intensively (see Kolmanovskii, V.B. and Nosov, V.R., Stability and Periodic Modes of Control Systems with Aftereffect; Nauka: Moscow, 1981 and Mao X., Stochastic Differential Equations and Their Applications; Horwood Pub.: Chichester, 1997). Given that many systems are often subject to component failures or repa...

On the Diffusive Nicholson's Blowflies Equation with Nonlocal Delay

This paper is concerned with the diffusive Nicholson’s blowflies model with nonlocal (or spatiotemporal) delay. When the spatial variable is one-dimensional, we establish the existence of travelling wave-front solutions by using the approach developed by Wang, Li, and Ruan (J. Differ. Equ. 222, 185–232, 2006) on the existence of travelling front solutions of reaction–diffusion systems with nonl...

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...