• Proceedings of the Korean Statistical Society Conference
• /
• 2005.11a
• /
• pp.55-58
• /
• 2005

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector-valued non-Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ${\hat{g}}$ for non-Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ${\hat{g}}$ First, it is shown that there are some cases when the asymptotic variance of ${\hat{g}}$ under non-Gaussianity can be smaller than that under Gaussianity. The result shows that non-Gaussianity of X(t) does not always affect worse. Second, we give a necessary and sufficient condition for ${\hat{g}}$ to be asymptotically efficient when the return process is Gaussian, which shows that ${\hat{g}}$ is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. We examine our approach numerically.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.141-152
• /
• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.1
• /
• pp.27-33
• /
• 2012

Let $f$ be a difeomorphism of a closed $n$ -dimensional smooth manifold M, and $p$ be a hyperbolic periodic point of $f$. Let ${\Lambda}(p)$ be a closed set which containing $p$. In this paper, we show that (i) if $f$ has the asymptotic average shadowing property on ${\Lambda}(p)$, then ${\Lambda}(p)$ is the chain component which contains $p$. (ii) suppose $f$ has the asymptotic average shadowing property on ${\Lambda}(p)$. Then if $f|_{\Lambda(p)}$ has the $C^{1}$-stably shadowing property then it is hyperbolic.

• Journal of Communications and Networks
• /
• v.15 no.6
• /
• pp.576-580
• /
• 2013

In this paper, we investigate the capacity of a multipoint-to-point cognitive radio network. In existing works, the asymptotic capacity is only obtained in the high peak power region at secondary transmitter (ST) or obtained without considering the interference from primary transmitter (PT) for easy analysis. Here, we analyze the asymptotic capacity by considering an arbitrary peak power at the ST and the interference from the PT based on extreme value theory. Simulation results show that our approximated capacity is well-matched to the exact capacity. Furthermore, the scaling law of our capacity is found to be double logarithm of the number of secondary users.

• International Journal of Reliability and Applications
• /
• v.4 no.4
• /
• pp.171-181
• /
• 2003

This paper proposes a U-test statistic for the problem of testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential on complete data. Selected critical values are tabulated for sample sizes n =5(1)60. The asymptotic normality of the statistic is proved and a comparison is made of the asymptotic efficiency between the statistic and other statistics. The power of the test is studied by simulation. A test for HNBUET in the case of randomly right-censored data is also considered. An application of the proposed test statistic in medical sciences is given.

• Multiscale and Multiphysics Mechanics
• /
• v.1 no.1
• /
• pp.15-33
• /
• 2016

In this paper, an asymptotic method is employed to formulate nano- or micro-beams based on strain gradient elasticity. Although a basic theory for the strain gradient elasticity has been well established in literature, a systematic approach is relatively rare because of its complexity and ambiguity of higher-order elasticity coefficients. In order to systematically identify the strain gradient effect, an asymptotic approach is adopted by introducing the small parameter which represents the beam geometric slenderness and/or the internal atomistic characteristic. The approach allows us to systematically split the two-dimensional strain gradient elasticity into the microscopic one-dimensional through-the-thickness analysis and the macroscopic one-dimensional beam analysis. The first-order beam problem turns out to be different from the classical elasticity in terms of the bending stiffness, which comes from the through-the-thickness strain gradient effect. This subsequently affects the second-order transverse shear stress in which the surface shear stress exists. It is demonstrated that a careful derivation of a first strain gradient elasticity embraces "Gurtin-Murdoch traction" as the surface effect of a one-dimensional Euler-Bernoulli-like beam model.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.21 no.8
• /
• pp.32-42
• /
• 2022

Asymptotic tracking of a non-minimum phase nonlinear system has been a popular topic in control theory and application. In this paper, we propose a new control scheme to achieve asymptotic output tracking in anon-minimum phase nonlinear system for periodic trajectories through an iterative learning control with the stable inversion. The proposed design method is robust to parameter uncertainties and periodic external disturbances since it is based on iterative learning. The performance of the proposed algorithm was demonstrated through the simulation results using a typical non-minimum nonlinear system of an inverted pendulum on a cart.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.233-245
• /
• 1997

In this paper, we study the asymptotic behavior of a random evolution. Some examples of random evolution can be found in Chapter 12 of [2].

• Journal of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.69-75
• /
• 1997

• The KIPS Transactions:PartA
• /
• v.10A no.1
• /
• pp.59-68
• /
• 2003

3-D data modeling of a volumetric scattered data is highly demanded for geological structure inspection, environment visualization and supersonic testing. The data used in these area are generally irregularly scattered in a volume data space, which are much different from the structured points data (cuberille data) used in Marching cube algorithm. In this paper, first we explore a volume modeling method for the scattered data based on tetrahedral domain. Next we propose a method for solving the ambiguity of tetrahedral domain decision using asymptotic decider criterion. Last we implement a simple visualization system based on the proposed asymptotic decider criterion and compare it with a system based on sphere criterion. In deciding tetrahedral domain, sphere criterion considers only positional values but asymptotic decider criterion considers not only positional values but also functional values, so asymptotic decider criterion is more accurate on deciding tetrahedral domain than sphere criterion.