Application of a Fast Simulation Scheme Having a Wide Applicability to Some Practical Fields Including Information Technologies

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1. We have succeeded in constructing a theoretical basis for an importance sampling simulation scheme for analyzing stochastic systems driven by compound Poisson processes. The basic principle is constructed from a rather general point of view by applying the Girsanov-Meyer theorem, which indicates that our proposed principle can be directly applied to stochastic systems driven by more general semimartingales. Further, we have constructed a concrete simulation scheme based upon it, whose efficiency is verified through some numerical examples.2. We have discussed to apply our method to some practical fields; (a) We have discussed application of our proposed simulation scheme to the Cramer-Lundberg model, which is most widely known in the collective risk theory, and clarified that our scheme works quite well for estimating small probability of default. Our discussion is based upon some mathematical analogies between the collective risk theory and the system reliability analysis. Therefor … More e, our result is expected to be applied to cross-sectional fields between them. (b) We have constructed a new probabilistic model for describing fatigue crack growth under random overloads by taking into account the crack growth retardation effect caused by large scale yielding generated by overloads. The basic equation of the proposed model is a system of random differential equation of Ito type driven by a compound Poisson process expressing the random overload process. (c) We have constructed a new probabilistic model for a traffic analysis in telecommunication networks by applying a system of Ito random differential equations driven by compound Poisson processes. Further, we have developed an importance sampling simulation scheme to estimate extremely small value for the bit-error rate.3. We have discussed void formations appearing in the process of via filling by a kinetic Monte Carlo simulation, which is based upon the Solid-by-Solid model originally developed by us. The results show that (i) small voids successively appear along a center line when a V-shaped via is filled and (ii) a long and large void appears in the center area when a rectangular via is filled, which have good agreements with some experimental results. Less