• Title, Summary, Keyword: Gaussian process

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CONDITIONAL TRANSFORM WITH RESPECT TO THE GAUSSIAN PROCESS INVOLVING THE CONDITIONAL CONVOLUTION PRODUCT AND THE FIRST VARIATION

  • Chung, Hyun Soo;Lee, Il Yong;Chang, Seung Jun
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1561-1577
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    • 2014
  • In this paper, we define a conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation of functionals via the Gaussian process. We then examine various relationships of the conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation for functionals F in $S_{\alpha}$ [5, 8].

Superior and Inferior Limits on the Increments of Gaussian Processes

  • Park, Yong-Kab;Hwang, Kyo-Shin;Park, Soon-Kyu
    • Journal of the Korean Statistical Society
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    • v.26 no.1
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    • pp.57-74
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    • 1997
  • Csorgo-Revesz type theorems for Wiener process are developed to those for Gaussian process. In particular, some results of superior and inferior limits for the increments of a Gaussian process are differently obtained under mild conditions, via estimating probability inequalities on the suprema of a Gaussian process.

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On Lag Increments Of A Gaussian Process

  • Choi, Yong-Kab;Choi, Jin-Hee
    • Communications of the Korean Mathematical Society
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    • v.15 no.2
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    • pp.379-390
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    • 2000
  • In this paper the limit theorems on lag increments of a Wiener process due to Chen, Kong and Lin [1] are developed to the case of a Gaussian process via estimating upper bounds of large deviation probabilities on suprema of the Gaussian process.

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ON THE INCREMENTS OF A d-DIMENSIONAL GAUSSIAN PROCESS

  • LIN ZHENGYAN;HWANG KYO-SHIN
    • Journal of the Korean Mathematical Society
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    • v.42 no.6
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    • pp.1215-1230
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    • 2005
  • In this paper we establish some results on the increments of a d-dimensional Gaussian process with the usual Euclidean norm. In particular we obtain the law of iterated logarithm and the Book-Shore type theorem for the increments of ad-dimensional Gaussian process, via estimating upper bounds and lower bounds of large deviation probabilities on the suprema of the d-dimensional Gaussian process.

GIRSANOV THEOREM FOR GAUSSIAN PROCESS WITH INDEPENDENT INCREMENTS

  • Im, Man Kyu;Ji, Un Cig;Kim, Jae Hee
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.4
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    • pp.383-391
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    • 2006
  • A characterization of Gaussian process with independent increments in terms of the support of covariance operator is established. We investigate the Girsanov formula for a Gaussian process with independent increments.

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ON THE LARGE AND SMALL INCREMENTS OF GAUSSIAN RANDOM FIELDS

  • Zhengyan Lin;Park, Yong-Kab
    • Journal of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.577-594
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    • 2001
  • In this paper we establish limit theorems on the large and small increments of a two-parameter Gaussian random process on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter Gaussian random process.

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STRASSEN'S FUNCTIONAL LIL FOR d-DIMENSIONAL SELF-SIMILAR GAUSSIAN PROCESS IN HOLDER NORM

  • HWANG, KYO-SHIN;LIN, ZHENGYAN
    • Journal of the Korean Mathematical Society
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    • v.42 no.5
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    • pp.959-973
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    • 2005
  • In this paper, based on large deviation probabilities on Gaussian random vectors, we obtain Strassen's functional LIL for d-dimensional self-similar Gaussian process in Holder norm via estimating large deviation probabilities for d-dimensional self-similar Gaussian process in Holder norm.

A TRANSLATION THEOREM FOR THE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE

  • Chang, Seung Jun;Choi, Jae Gil;Ko, Ae Young
    • Journal of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.991-1017
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    • 2016
  • In this paper we define a generalized analytic Fourier-Feynman transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier-Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.

A Study on Fatigue Analysis of Non-Gaussian Wide Band Process using Frequency-domain Method (주파수 영역 해석 기법을 이용한 비정규 광대역 과정의 피로해석에 관한 연구)

  • Kim, Hyeon-Jin;Jang, Beom-Seon
    • Journal of the Society of Naval Architects of Korea
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    • v.55 no.6
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    • pp.466-473
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    • 2018
  • Most frequency domain-based approaches assume that structural response should be a Gaussian random process. But a lot of non-Gaussian processes caused by multi-excitation and non-linearity in structural responses or load itself are observed in many real engineering problems. In this study, the effect of non-Normality on fatigue damages are discussed through case study. The accuracy of four frequency domain methods for non-Gaussian processes are compared in the case study. Power-law and Hermite models which are derived for non-Gaussian narrow-banded process tend to estimate fatigue damages less accurate than time domain results in small kurtosis and in case of large kurtosis they give conservative results. Weibull model seems to give conservative results in all environmental conditions considered. Among the four methods, Benascuitti-Tovo model for non-Gaussian process gives the best results in case study. This study could serve as background material for understanding the effect of non-normality on fatigue damages.