• 제목/요약/키워드: control limit theorems

검색결과 3건 처리시간 0.02초

CENTRAL LIMIT THEOREMS FOR BELLMAN-HARRIS PROCESSES

  • Kang, Hye-Jeong
    • 대한수학회지
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    • 제36권5호
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    • pp.923-943
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    • 1999
  • In this paper we consider functionals of the empirical age distribution of supercritical Bellman-Harris processes. Let f : R+ longrightarrow R be a measurable function that integrates to zero with respect to the stable age distribution in a supercritical Bellman-Harris process with no extinction. We present sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

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Modified z-변환의 성질상의 해석적 문제점 (Analytic Problems of the Properties of the Modified z-Transform)

  • 정태상;장태규;이영운;김형준
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1996년도 추계학술대회 논문집 학회본부
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    • pp.39-41
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    • 1996
  • While the z-transform method is a basic mathematical tool to relate the signals only at the sampling instants in analyzing and designing sampled-data control systems, the modified z-transform which is a variation of the z-transform is widely used to represent the details of continuous signals between the sampling instants. Regarding the modified z-transform method, some properties were established to relate the modified z-transform to the regular z-transform. This paper will show that these properties, in their current forms, cause some analytic problems, when they are applied to the signals with discontinuities at the sampling instants, which accordingly limit their applications significantly. In this paper, those analytic problems will be investigated, and the theorems of the modified z-transform will be revised by adopting a new notation so that those can be correctly interpreted and used without any analytic problems in the analysis of sampled data systems. Also some useful schemes of applying the modified z-transform will be developed.

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변형 Z변환의 특헝의 적용상의 해석적 문제 (Analytic Problems in Applying the Properties of teh Modified z-Transform)

  • 정태상;이재석
    • 대한전기학회논문지:시스템및제어부문D
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    • 제51권12호
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    • pp.549-555
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    • 2002
  • While the z-transform method is a basic mathematical tool to relate the imput/output signals only at the sampling instants in analyzing and designing sampled-data control systems, the modified z-transform which is a variation of the z-transform is widely used to represent the details of continuous signals between the sampling instants. To relate the modified z-transform to the corresponding regular z-transform, some properties were established regarding the modified z-transform method. This paper will show that these properties, in their current forms, cause come analytic problems, when they are applied to the signals with discontinuities at the sampling instants, which accordingly limit their applications significantly. In this paper, those analytic problems will be investigated, and the theorems of the modified z-transform will be revised by adopting new notations on the z-transform so that those can be correctly interpreted and used without any analytic problems. Also some additional useful schemes of applying the modified z-transform will be developed.