In this paper, we consider a stochastic SIS epidemic model with vaccination. We prove that the densities of the distributions of the solution can converge in L1 to an invariant density under appropriate conditions. Also we find the support of the invariant density.

In this paper, we discuss the dynamics of a stochastic SIS epidemic model with vaccination. When the noise is large, the infective decays exponentially to zero regardless of the magnitude of R0. When the noise is small, sufficient conditions for extinction exponentially and persistence in the...

This paper proposes a semiparametric method for an autoregressive model by combining a parametric regression estimator with a nonparametric adjustment. The regression has a parametric framework. After the parameter is estimated through a general parametric method, the obtained regression...

In this paper, we study a stationary ARCH(q) model with parameters &agr;_0,&agr;_1,&agr;_2, H ,&agr;_q. It is known that the model requires all parameters &agr;_i to be non-negative, but sometimes the usual algorithm based on Newton-Raphson's method leads us to obtain some negative solutions. So this study proposes...

In this paper, we study a stationary ARCH(q) model with parameters x(0),x(1), x(2), . . ., x(q). It is known that the model requires all parameters to be non-negative, but sometimes the usual algorithm based on Newton-Raphson's method leads us to obtain some negative solutions. So this study...