Ruin probabilities of small noise jump‐diffusions with heavy tails

Let X^ε(x) be a solution of a stochastic differential equation , where L is a Lévy process with heavy tails. In the limit of the scale parameter ε ↓ 0 we determine the finite horizon ruin probability P . Copyright © 2007 John Wiley & Sons, Ltd.     

Controller design for network‐based Markovian jump systems with unreliable communication links

This article is concerned with observer and controller design for networked control systems, where the considered plant refers to a class of discrete‐time communication delay Markovian jump systems. In the study, random packet losses and output quantization are considered simultaneously. The packet losses considered here includes sensor to controller and controller to actuator sides, which are modeled as two Bernoulli distributed white sequences, respectively. An observer‐based control scheme is developed to stabilize the closed‐loop systems. Finally, an illustrative example is provided to show the applicability of the proposed control method. © 2016 Wiley Periodicals, Inc. Complexity 21: 623–634, 2016     

Stabilization of active fault‐tolerant control systems by uncertain nonhomogeneous markovian jump models

This article investigates the stabilization and control problems for a general active fault‐tolerant control system (AFTCS) in a stochastic framework. The novelty of the research lies in utilizing uncertain nonhomogeneous Markovian structures to take account for the imperfect fault detection and diagnosis (FDD) algorithms of the AFTCS. The underlying AFTCS is supposed to be modeled by two random processes of Markov type; one characterizing the system fault process and the other describing the FDD process. It is assumed that the FDD algorithm is imperfect and provides inaccurate Markovian parameters for the FDD process. Specifically, it provides uncertain transition rates (TRs); the TRs that lie in an interval without any particular structures. This framework is more consistent with real‐world applications to accommodate different types of faults. It is more general than the previously developed AFTCSs because of eliminating the need for an accurate estimation of the fault process. To solve the stabilizability and the controller design problems of this AFTCS, the whole system is viewed as an uncertain nonhomogeneous Markovian jump linear system (NHMJLS) with time‐varying and uncertain specifications. Based on the multiple and stochastic Lyapunov function for the NHMJLS, first a sufficient condition is obtained to analyze the system stabilizability and then, the controller gains are synthesized. Unlike the previous fault‐tolerant controllers, the proposed robust controller only needs to access the FDD process, besides it is easily obtainable through the existing optimization techniques. It is successfully tested on a practical inverted pendulum controlled by a fault‐prone DC motor. © 2016 Wiley Periodicals, Inc. Complexity 21: 318–329, 2016     

Bayesian sequential testing for Lévy processes with diffusion and jump components

We study the Bayesian problem of sequential testing of two simple hypotheses about the Lévy-Khintchine triplet of a Lévy process, having diffusion component, represented by a Brownian motion with drift, and jump component of finite variation. The method of proof consists of reducing the original optimal stopping problem to a free-boundary problem. We show it is characterized by a second order integro-differential equation, that the unknown value function solves on the continuation region, and by the smooth fit principle, which holds at the unknown boundary points. Several examples are presented.     

A randomized first-passage problem for drifted Brownian motion subject to hold and jump from a boundary

We study an inverse first-passage-time problem for Wiener process X(t) subject to hold and jump from a boundary c. Let be given a threshold S > X(0) ≥ c, and a distribution function F on [0, +∞). The problem consists in finding the distribution of the holding time at c and the distribution of jumps from c, so that the first-passage time of X(t) through S has distribution F.     

The numbers of jump layers of boundary value problems in quasilinear differential equations

This paper discusses the numbers of jump layers of boundary value problems in quasilinear differential equations. In addition, the paper gives several examples to explain why the original equation must be rediscussed when the determinate function in reference [1] is always equal to zero.     

Large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure

Basic equations for large deflection theory of thin orthotropic circular plate with variable thickness are derived in this paper. The modified iteration method is adopted to solve the large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure. If ε=0, then the solution derived from the result in this paper coincides completely with the result given by J. Nowinski (using perturbation method) for solving large deflection problem of thin orthotropic circular plate with constant thickness under uniform pressure.     

氮氧自由基中的多光子化学反应(Ⅰ)

在不同光源照射下,作者利用乙基亚硝基有机化合物在乙醇溶剂下,产生双光子的化学反应,用电子自旋共振吸收谐振腔为反应器.在不同的流速下,生成3种同分异构自由基.其结构由电子自旋共振光谱确定、微观的氢键跳动频率由不同波形的氮核超精细偶合常数的变化而确定、利用Charm软件计算,确定β-氢超精细偶合常数的意义及其几何形状.     

The study of chamber rockburst by the CUSP model of catastrophe theory

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