Exponential Bounds for Ruin Probability in Two Moving Average Risk Models with Constant Interest Rate

The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.

EXPONENTIALLY BOUNDED C-SEMIGROUP AND INTEGRATED SEMIGROUP WITH NONDENSELY DEFINED GENERATORS I: APPROXIMATION:

In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.

Sampled-data Observer Design for a Class of Stochastic Nonlinear Systems Based on the Approximate Discrete-time Models

In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.

The generators of exponentially bounded C-semigroups and theHille-Yosida spaces

Let（X,||·||）be a Banach space and let C be an injective bounded linear operator inX.A strongly continuous family of bounded linear operators{S（t）;t≥0}is called anexponentially bounded C-semigroup（hereinafter abbreviated to C-semigroup）on X,if S（0）=C,S（t）S（s）=S（t+s）C,t,s≥0,and ||S（t）||≤Meat,t≥0.

MODEL SELECTION FOR LOG-LINEAR MODELS OF CONTINGENCY TABLES

In this paper, we propose an information-theoretic-criterion-based modelselection procedure for log-linear model of contingency tables under multinomial sampling, andestablish the strong consistency of the method under some mild conditions. An exponential bound ofmiss detection probability is also obtained. The selection procedure is modified so that it can beused in practice. Simulation shows that the modified method is valid. To avoid selecting the penaltycoefficient in the information criteria, an alternative selection procedure is given.