• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.131-149
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• 2010

In 1992, the author introduced the definition and the properties of Wiener measure over paths in Wiener space and this measure was investigated extensively by some mathematicians. In 2002, the author and Dr. Im presented an article for analogue of Wiener measure and its applications which is the generalized theory of Wiener measure theory. In this note, we will derive the analogue of Wiener measure over paths in Wiener space and establish two integration formulae, one is similar to the Wiener integration formula and another is similar to simple formula for conditional Wiener integral. Furthermore, we will give some examples for our formulae.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} if $Y_{j}$ > $Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, n$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.451-470
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• 2020

Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition 0 = t₀ < t₁ < ⋯ < t_n < t_n+1 = T of [0, T], define X_n : C[0, T] → ℝⁿ⁺¹ by X_n(x) = (x(t₀), x(t₁), …, x(t_n)). In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function X_n which has a drift and does not contain the present position of paths. As applications of the formula with X_n, we evaluate the Radon-Nikodym derivatives of the functions ∫₀^T[x(t)]^mdλ(t)(m∈ℕ) and [∫₀^Tx(t)dλ(t)]² on C[0, T], where λ is a complex-valued Borel measure on [0, T]. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on C[0, T].

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.311-317
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• 2001

It is necessary to check the linearity of selected covariates in regression diagnostics. There are various graphical methods using residual plots such as partial residual plots, augmented partial residual plots and combining conditional expectation and residual plots. In this paper, we propose the modified pseudolikelihood ratio test statistics based on these residual plots to test linearity of selected covariate. These test statistics which measure the distance between the nonparametric and parametric models are derived as a ratio of quadratic forms. The approximate distribution of these statistics is calculated numerically by using three moments. The power comparison of these statistics is given.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.793-803
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• 2010

In this note, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $L^2(\cal{F})$ such as, p-quasihyponormal, p-paranormal, p-hyponormal and weakly hyponormal. Some examples are then presented to illustrate that weighted composition operators lie between these classes.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.71-77
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• 1999

We show that if the stable rank of $B^{\alpha}$ is one, then the stable rank of B is less than or equal to the order of G for any action of a finite group G. Also we give a short proof to the known fact that if the action of a finite group on a $C^*$-algebra B is saturated then the canonical conditional expectation from B to $B^{\alpha}$ is of index-finite type and the crossed product $C^*$-algebra is isomorphic to the algebra of compact operators on the Hilbert $B^{\alpha}$-module B.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.579-586
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• 2009

Let $\varphi$ be a complete probability measure on $\mathbb{R}$, let $m_{\varphi}$ be the analogue of Wiener measure over paths on [0, T] and let f(t) be continuously differentiable on [0, T]. In this note, we give the analogue of Wiener measure $m_{\varphi}$ of {x in C[0, T]$\mid$x(0) < f(0) and $x(s_0){\geq}f(s_{0})$ for some $s_{0}$ in [0, T]} by use of integral equation techniques. This result is a generalization of Park and Paranjape's 1974 result[1].

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.347-361
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• 2014

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto or Lomax distribution. In this paper, we established exact expressions and recurrence relations satised by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.8
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• pp.3498-3511
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• 2016

We investigate the channel state information (CSI) in multi-input multi-output (MIMO) cooperative networks that employ the amplify-and-forward transmission scheme. Least squares and expectation conditional maximization have been proposed in the system. However, neither of these two approaches takes advantage of channel sparsity, and they cause estimation performance loss. Unlike linear channel estimation methods, several compressed channel estimation methods are proposed in this study to exploit the sparsity of the MIMO cooperative channels based on the theory of compressed sensing. First, the channel estimation problem is formulated as a compressed sensing problem by using sparse decomposition theory. Second, the lower bound is derived for the estimation, and the MIMO relay channel is reconstructed via compressive sampling matching pursuit algorithms. Finally, based on this model, we propose a novel algorithm so called sparsity adaptive expectation maximization (SAEM) by using Kalman filter and expectation maximization algorithm so that it can exploit channel sparsity alternatively and also track the true support set of time-varying channel. Kalman filter is used to provide soft information of transmitted signals to the EM-based algorithm. Various numerical simulation results indicate that the proposed sparse channel estimation technique outperforms the previous estimation schemes.

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
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• v.15 no.3
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• pp.19-32
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• 2020

This study analyzed the effects of ICT technical characteristics of agricultural industry on smart farm entrepreneurial intention by using smart farm effort expectation and smart farm acceptance intention as mediators for smart farm pre-founders. Sub-variables of the technical characteristics of agricultural industry ICT were classified into availability, economics, data convergence and scalability. 349 questionnaires collected from pre-founders living in the country were used for empirical analysis. SPSS v22.0 and Process macro v3.4 were used to analyze the data based on serial multiple mediation model. First, economics and scalability had a positive (+) effect on start-up intention. Second, availability, economics and scalability had a significant effect on effort expectation. Third, effort expectation had a significant positive effect on acceptance intention. Fourth, acceptance intention had a significant positive effect on start-up intention. Fifth, the indirect effects of economics on start-up intention were all significant through effort expectation, through acceptance intention and through both effort expectation and acceptance intention. Sixth, the indirect effect of data convergence on start-up intention was significant through acceptance intention. Seventh, the indirect effect of scalability on start-up intention was significant through effort expectation and through both effort expectation and acceptance intention. As a follow-up study, it is necessary to study for the mediating variables other than mediators introduced in the study or the moderated mediation analysis through the conditional process model in which the moderating variable is introduced.