In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo-maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$100 (1-\alpha )\%$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>100</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>-</mo> <mi mathvariant="italic">α</mi> <mo stretchy="false">)</mo> <mo>%</mo> </mrow> </math> </EquationSource> </InlineEquation> confidence intervals as well as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$100...</equationsource></inlineequation></equationsource></equationsource></inlineequation>

In this paper we shall establish a new theorem on the existence and uniqueness of the adapted solution to a backward stochastic differential equation under a weaker condition than the Lipschitz one.

Stability of stochastic differential equations with Markovian switching has recently been discussed by many authors, for example, Basak et al. (J. Math. Anal. Appl. 202 (1996) 604), Ji and Chizeck (IEEE Trans. Automat. Control 35 (1990) 777), Mariton (Jump Linear System in Automatic Control,...

The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching. Linear NSDDEs with Markovian switching and nonlinear examples will be discussed to illustrate the theory.

Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semi-linear type of such equations has been studied by Basak et al. (1996, J. Math. Anal. Appl. 202, 604-622), Ji and Chizeck (1990, Automat....

Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic...

Stochastic differential equations with Markovian switching (SDEwMSs), one of the important classes of hybrid systems, have been used to model many physical systems that are subject to frequent unpredictable structural changes. The research in this area has been both theoretical and applied. Most...

Consider a stochastic differential equation with respect to semimartingales dX(t)=AX(t)d[mu](t)+G(X(t),t) dM(t) which might be regarded as a stochastic perturbed system of dX(t)=AX(t)d[mu](t). Suppose the second equation is exponentially stable almost surely. What we are interested in in this...