• Honam Mathematical Journal
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• v.30 no.4
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• pp.723-732
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• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.18-21
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• 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.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.699-705
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• 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).

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.359-381
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• 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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.385-396
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• 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.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.485-489
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• 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.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.833-848
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• 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
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• v.32 no.1
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• pp.55-69
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• 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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.149-153
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• 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.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.6
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• pp.121-132
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• 2005

In the formation of images in a camera, the exposure time is appropriately adjusted to obtain a good image. Hence for a successful alignment of a sequence of images to the same scene, it is required to compensate the different exposure times. If we have no knowledge regarding the exposure time, then we should develop an algorithm that can compensate an image with respect to a reference image without using any camera formation models. In this paper, an exposure compensation is performed by designing predictors based on the conditional expectation between the reference and input images. Further, an adaptive predictor design is conducted to manage the irregular exposure or histogram problem. In order to alleviate the blocking artifact and the overfitting problems in the adaptive scheme, a smoothing technique, which uses the pixels of the adjacent blocks, is proposed. We successfully conducted the exposure compensation using real images obtained from digital cameras and the transmission electron microscopy.