Papers by Keyword: Poisson Process

Abstract: The structure of the estimators is similar to the recursive kernel estimators of a density function and its derivative. The estimators have been constructed using a single realization of Poisson process on a fixed time interval. Mean-square convergence has been proved in a scheme of series. Simulation studies have been carried out to illustrate the convergence.

Abstract: In this paper, it aims at an n-year term increasing life insurance model, considers the factual statements and the bursting out things’ influence on interest rate, establishes the model for stochastic interest rate by Reflected Brownian motion associating with Poisson process, and gives the common expression of semi-continuous reserve and the expression in the suppose of Uniform distribution of death.

Abstract: The problem of optimal dynamic allocation of resources in security should be built in such a manner to include the impact assessment of rare events, such as natural or asymmetric extreme events. This paper presents a model for the analysis of investment situations that involves real options with multiple sources of jump risk and identification of management solutions that increase the value of the investment opportunity using Wiener processes and Poisson distribution. The results are solutions for improved decision-making in aviation systems.

Abstract: Stress-strength interference model has been widely used for reliability analysis of structures.Strength degradation of a structure is a common phenomenon in engineering. To evaluate the structure reliability in the case of strength degradation over time, the strength degradation is represented by a gamma process and the stress applied on a structure is represented by the Poisson process in this paper. Then a time-dependent stress-strength interference model is suggested by employing numerical integration method. With this model, the structure reliability can be evaluated more accurately.

Abstract: A GLR (generalized likelihood ratio) chart for Poisson distributed process with individual observations is proposed and the design procedure of the GLR chart is discussed. The performance of the GLR charts is compared to the exponentially weighted moving average (EWMA) chart and the GWMA chart. The numerical experiments show that the GLR chart has comparable performance as the other two charts. However, the GLR chart is much easier to design and implement since there are more design parameters in these two charts.

Abstract: A system at inception is endowed with a random amount of resource, the process of the lapse of system life can be viewed as that of the depletion of random resource caused by the wear-out effect. This thesis considers the wear-out process of the system as the sum of an additive compound nonhomogeneous poisson shock wear-out and a continuous routine wear-out in time t. With the introduction of the concept of random resource, a wear-out model is built. Moreover, the aging properties of the system lifetime are studied in this model.

Abstract: In this paper, we examine an optimal impulse control problem of stochastic system, whose state follows a Brownian motion. Here we want to maximum the objective function. The main feature of our model is that the controlled state process includes an impulse control governed by a Poisson process. In other words, the set of possible intervention times are discrete, random and determined by the signal process. Here we not only present a theorem giving a sufficient condition on the existence of an optimal control and its corresponding objective function, but also provide an explicit solution obtained under some simplified conditions.

Abstract: We consider a manufacturing system which takes vacation and subjects to breakdown. Items arrive to the production facility according to a compound Poisson process. Using supplementary variables we determine the probability generating function (p.g.f) of the system size. Under the Long Run Average Cost formulation, we show that the optimal vacation policy is either single or multiple vacation policy.

Abstract: In this paper, we study the Gerber-Shiu discounted penalty function. We shall consider the case where the discount interest process and the occurrence of the claims are driven by two distinguished Markov process, respectively. Moreover, in this model we also consider the influence of a premium rate which varies with the level of free reserves. Using backward differential argument, we derive the integral equation satisfied by the expected discounted penalty function via differential argument when interest process in every state is perturbed by standard Wiener process and Poisson process. In some special cases, closed form expression for these quantities are obtained.