• Communications for Statistical Applications and Methods
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• v.17 no.1
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• pp.47-54
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• 2010

By using the white noise theory for fractional Brownian sheet, we give new representations of the Wick integrals of various types with respect to fractional Brownian sheet with Hurst parameters $H_1,H_2{\in}$(0, 1).

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.631-648
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• 2019

In this paper, we consider a semilinear stochastic heat equation driven by an additive fractional white noise. Under the pathwise uniqueness property, we establish various strong stability results. As a consequence, we give an application to the convergence of the Picard successive approximation.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.173-178
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• 2005

We derive an It${\hat{o}}$ formula for generalized functionals for the fractional Brownian sheet with arbitrary Hurst parameter ${H_1},\;H_2$ ${\epsilon}$ (0,1). As an application, we consider a stochastic integral representation for the local time of the fractional Brownian sheet.

• ETRI Journal
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• v.45 no.1
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• Journal of Biomedical Engineering Research
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• v.25 no.6
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• pp.439-445
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• 2004

Diffusion tensor image(DTI) exploits the random diffusional motion of water molecules. This method is useful for the characterization of the architecture of tissues. In some tissues, such as muscle or cerebral white matter, cellular arrangement shows a strongly preferred direction of water diffusion, i.e., the diffusion is anisotropic. The degree of anisotropy is often represented using diffusion anisotropy indices (relative anisotropy(RA), fractional anisotropy(FA), volume ratio(VR)). In this study, FA images were obtained using different gradient schemes(N=6, 11, 23, 35. 47). Mean values and the standard deviations of FA were then measured at several anatomic locations for each scheme. The results showed that both mean values and the standard deviations of FA were decreased as the number of gradient directions were increased. Also, the standard error of ADC measurement decreased as the number of diffusion gradient directions increased. In conclusion, different gradient schemes showed a significantly different noise performance and the schem with more gradient directions clearly improved the quality of the FA images. But considering acquisition time of image and standard deviation of FA, 23 gradient directions is clinically optimal.