• 호남수학학술지
• /
• 제30권4호
• /
• pp.723-732
• /
• 2008

In this note, we establish the uniqueness theorem of conditional expectation on analogue of Wiener measure space for given distributions and prove the simple formula of conditional expectation on analogue of Wiener measure which is essentially similar to Park and Skoug's formula on the concrete Wiener measure.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
• /
• pp.18-21
• /
• 2003

We propose some properties of fuzzy conditional expectation of hybrid number the addition of fuzzy number and random variable using Cartesian product distance for ${\alpha}$-level sets.

• 대한수학회지
• /
• 제36권4호
• /
• pp.699-705
• /
• 1999

Given a probability space and a subsigma algebra A, each measure equivalent to the probability measure generates a different conditional expectation operator. We characterize those which act boundedly on the original $L^2$ space, and show there are sufficiently many such conditional expectations to generate the commutant of $L^{\infty}$ (A).

• 대한수학회지
• /
• 제57권2호
• /
• pp.359-381
• /
• 2020

In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued Lévy's martingale convergence theorem are proved by using the Slice and the linear topologies.

• 충청수학회지
• /
• 제29권3호
• /
• pp.385-396
• /
• 2016

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

• 대한수학회논문집
• /
• 제25권3호
• /
• pp.485-489
• /
• 2010

A family of continuous probability distribution has been characterized through the difference of two conditional expectations, conditioned on a non-adjacent record statistic. Also, a result based on the unconditional expectation and a conditional expectation is used to characterize a family of distributions. Further, some of its deductions are also discussed.

• 대한수학회지
• /
• 제55권4호
• /
• pp.833-848
• /
• 2018

In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued $L{\acute{e}}vy^{\prime}s$ martingale convergence theorem for integrable and Pettis integrable random sets are proved.

• Structural Engineering and Mechanics
• /
• 제32권1호
• /
• pp.55-69
• /
• 2009

A quasi ideal importance sampling simulation method combined in the conditional expectation is proposed for the structural reliability estimation. The quasi ideal importance sampling joint probability density function (p.d.f.) is so composed on the basis of the ideal importance sampling concept as to be proportional to the conditional failure probability multiplied by the p.d.f. of the sampling variables. The respective marginal p.d.f.s of the ideal importance sampling joint p.d.f. are determined numerically by the simulations and partly by the piecewise integrations. The quasi ideal importance sampling simulations combined in the conditional expectation are executed to estimate the failure probabilities of structures with multiple failure surfaces and it is shown that the proposed method gives accurate estimations efficiently.

• 충청수학회지
• /
• 제22권2호
• /
• pp.149-153
• /
• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

• 대한전자공학회논문지SP
• /
• 제42권6호
• /
• pp.121-132
• /
• 2005

사진기에서 고품질의 영상을 획득하기 위해서는 적절히 노출 시간을 조절하게 되는데 이로 인해 각각 독립적으로 얻어진 영상들의 노출 시간은 서로 달라진다. 이는 여러 영상의 열을 정렬하는 과정 등에서 부정확한 결과를 초래할 수 있으므로 영상들의 노출 시간을 동일하게 맞추어 줄 필요가 있다. 그런데, 노출 시간을 알지 못하는 경우에는, 하나의 영상을 기준으로 다른 영상들의 상대적 노출 시간을 추정하고 보정하는 알고리즘에 대한 연구가 필요하다. 본 논문에서는, 사진기의 모델 함수를 고려할 필요 없는, 최소 오류 개념에서 최적의 예측기인 conditional expectation을 사용하여 노출 보정을 시도하였다. 나아가서, 불규칙한 노출 또는 히스토그램 특성을 위한 적응 노출 보정 기법을 제안하였다. 이때 blocking artifact 및 overfitting 등의 문제를 완화시키기 위한 인접의 화소를 사용하는 기법을 도입하였다. 디지털 사진기 및 투과전자현미경을 통하여 얻어진 실제 영상을 사용한 모의실험을 통하여 성공적인 노출 보정 수행을 확인할 수 있었다.