Exponential ergodicity of some Markov dynamical systems with application to a Poisson-driven stochastic differential equation

We are concerned with the asymptotics of the Markov chain given by the post-jump locations of a certain piecewise-deterministic Markov process with a state-dependent jump intensity. We provide sufficient conditions for such a model to possess a unique invariant distribution, which is exponentially attracting in the dual-bounded Lipschitz distance. Having established this, we generalize a result of J. Kazak on the jump process defined by a Poisson-driven stochastic differential equation with a solution-dependent intensity of perturbations.     

Response spectral density of linear systems with external and parametric non-Gaussian, delta-correlated excitation

An exact, closed form, analytical expressions for a response spectral density of a certain type of systems, subjected to non-Gaussian, stationary, delta-correlated noise are derived. A new, extended mean square stability conditions are derived for such systems.     

Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals

 Fractional differential equations of degree 1<α<2 are considered in this paper. A summary of numerical schemes for the time-domain solution of such problems is given. While all these methods require evaluation of the history of the state variables, an alternative concept recently published by Yuan and Agrawal (2002), which is computationally more efficient, is further developed. This scheme is based on a transformation of the original integro-differential problem into a system of linear differential equations. Here, parallels to the theory of internal variables are drawn. Received: 18 June 2002 / Accepted: 12 July 2002     

具拟线性扩散系数的脉冲中立型抛物系统的(强)振动性

研究一类具拟线性扩散系数的脉冲中立型抛物偏微分系统解的(强)振动性, 直接利用振动的定义、Green公式和Newmann边值条件将这类脉冲中立型抛物系统的振动问题转化为脉冲中立型微分不等式不存在最终正解的问题, 并利用最终正解的定义和脉冲中立型微分不等式, 获得了该类系统(强)振动的充分判据. 所得结果充分反映了脉冲和时滞在振动中的影响作用.     

Analytical method for reliability and MTTF assessment of coherent systems with dependent components

This paper discusses engineering systems with structural as well as failure dependence among their components. Using the Markov process approach, a coherent system of components with multivariate phase type life distribution is introduced to model the components working in a common random environment. The phase type model is flexible enough to comprise many realistic situations, and also manages to yield the explicit matrix representations of the system reliability measures. Some examples are also presented to illustrate the fact that ignoring the failure dependence among the components often results in over-estimating or under-estimating the system reliability.