• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.207-224
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• 1998

After the review of known results on the connections between selfsimilar processes with independent increments (processes of class L) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bound sets. Comparison in transience-recurrence of the Levy process and the process of class L associated with a common distribution of class L is made.

• 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.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.115-118
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• 2000

In this paper we establish limit results on the increments of (N, d)-Gaussian processes with independent components, via estimating upper bounds of large deviation probabilities on the suprema of (N, d)-Gaussian processes.

• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.93-111
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• 1993

Let ${X(t) : t \geq 0}$ be a real-valued stochastics process with stationary independent increments. In this paper, under the condition of stochastic compactness, we obtain appropriate function $\alpha(t)$ and random function $\beta(t)$ such that for some positive finite constant C, lim sup${X(t) - \alpha(t)}/\beta(t) = C$ a.s. both as t tends to zero and infinity.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.2-8
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• 2013

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.25-35
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• 2001

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to the stationary with independent increments and positive recurrent. We find some sufficient conditions for he Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.100-109
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• 1983

Let ${X_i}$ be a process with stationary and independent increments whose log characteristic function is expressed as $ibut-2^{-1}\sigma^2u^2t+t\int_{{0 }^c}{(exp(iux)-1-iux(i+x^2)^{-1})dv(x)}$. Our main result is taht $x^2(\int_{\y\>x}{dv(y)})/(\int_{$\mid$y$\mid$\leqx}{y^2dv(y)+\sigma^2}) \to 1$ as $x \to 0 (resp. x \to \infty)$ is necessary, and sufficient for ${X-i}$ to have ${A_t}$ and ${B_t}$ such that $(X_t-A_t)/B_t \to^D n(0,1)$ as $t \to 0 (resp. t \to \infty)$.

• Journal of the Korean Statistical Society
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• v.17 no.1
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• pp.30-45
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• 1988

Let ${X(t) : 0 \leq t < \infty}$ be a real-valued process with stationary independent increments. In this paper, we obtain necesary and sufficint condition for there to exist a positive, nondecreasing function $\beta(t)$ so that $0 < lim sup $\mid$X(t)$\mid$/\beta(t) < \infty$ a.s. both as t tends to zero and infinity. When no such $\beta(t)$ exists we give a simple integral test for whether $lim sup $\mid$X(t)$\mid$/\beta(t)$ is zero or infinity for a given $\beta(t)$.

• ALGAE
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• v.22 no.2
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• pp.107-116
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• 2007

Annual growth segments of Ascophyllum nodosum (L.) Le Jolis (Fucales, Fucaceae) are denoted by air bladders that form each spring. By examining annual growth segments, it may be possible to infer information about the physical conditions during the growth period; however, it is uncertain whether the annual segments will expand in size after the initial growth. We examined A. nodosum segments from three populations in Nova Scotia, and statistically evaluated whether the annual growth (length, mass, and maximum diameter) of segments was independent of the age of the frond, whether the segments increased in size after the initial growth, and whether the segment lengths were correlated with mean water temperatures and mean air temperatures when the segments were formed. We found that the growth in length of A. nodosum is dependent on the age of the frond, but frond age explained less than 12 % of the overall variation in length. However, the mass and maximum diameter of segments were independent of the age of the frond. Differences occurred between the lengths of segments formed in different years, but there was no significant correlation with regional mean water or air temperatures. This study indicates that the length of A. nodosum segments may be an indicator of the annual physical characteristics of a site, but future studies are needed to identify which factors have the strongest influence on growth patterns.

• Steel and Composite Structures
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• v.34 no.6
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• pp.877-889
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• 2020

This work features the outcomes of an empirical investigation into the characteristics of steel reinforced grout (SRG) composite - concrete interfaces. The parameters varied were loading rate, densities of steel fibres and types of load displacement responses or measurements (slip and machine grips). The following observations and results were derived from standard single-lap shear tests. Interfacial debonding of SRG - concrete joints is a function of both fracture of matrix along the bond interface and slippage of fibre. A change in the loading rate results in a variation in peak load (P_max) and the correlative stress (σ_max), slip and machine grips readings at measured peak load. Further analysis of load responses revealed that the behaviour of load responses is shaped by loading rate, fibre density as well as load response measurement variable. Notably, the out-of-plane displacement at peak load increased with increments in load rates and were independent of specimen fibre densities.