Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
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Stochastic convexity in Markov additive processes and its applications

마코프 누적 프로세스에서의 확률적 콘벡스성과 그 응용

  • Published : 1991.06.01
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Abstract

Stochastic convexity (concavity) of a stochastic process is a very useful concept for various stochastic optimization problems. In this study we first establish stochastic convexity of a certain class of Markov additive processes through probabilistic construction based on the sample path approach. A Markov additive process is abtained by integrating a functional of the underlying Markov process with respect to time, and its stochastic convexity can be utilized to provide efficient methods for optimal design or optimal operation schedule wide range of stochastic systems. We also clarify the conditions for stochastic monotonicity of the Markov process. From the result it is shown that stachstic convexity can be used for the analysis of probabilitic models based on birth and death processes, which have very wide applications area. Finally we demonstrate the validity and usefulness of the theoretical results by developing efficient methods for the optimal replacement scheduling based on the stochastic convexity property.

Keywords

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