• Title, Summary, Keyword: asymptotics

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PRECISE ASYMPTOTICS OF MOVING AVERAGE PROCESS UNDER ?-MIXING ASSUMPTION

  • Li, Jie
    • Journal of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.235-249
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    • 2012
  • In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.

GENERAL LAWS OF PRECISE ASYMPTOTICS FOR SUMS OF RANDOM VARIABLES

  • Meng, Yan-Jiao
    • Journal of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.795-804
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    • 2012
  • In this paper, we obtain two general laws of precise asymptotics for sums of i.i.d random variables, which contain general weighted functions and boundary functions and also clearly show the relationship between the weighted functions and the boundary functions. As corollaries, we obtain Theorem 2 of Gut and Spataru [A. Gut and A. Sp$\check{a}$taru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000), no. 4, 1870-1883] and Theorem 3 of Gut and Sp$\check{a}$taru [A. Gut and A. Sp$\check{a}$taru, Precise asymptotics in the Baum-Katz and Davids laws of large numbers, J. Math. Anal. Appl. 248 (2000), 233-246].

PRECISE ASYMPTOTICS FOR THE MOMENT CONVERGENCE OF MOVING-AVERAGE PROCESS UNDER DEPENDENCE

  • Zang, Qing-Pei;Fu, Ke-Ang
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.585-592
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    • 2010
  • Let {$\varepsilon_i:-{\infty}$$\infty$} be a strictly stationary sequence of linearly positive quadrant dependent random variables and $\sum\limits\frac_{i=-{\infty}}^{\infty}|a_i|$<$\infty$. In this paper, we prove the precise asymptotics in the law of iterated logarithm for the moment convergence of moving-average process of the form $X_k=\sum\limits\frac_{i=-{\infty}}^{\infty}a_{i+k}{\varepsilon}_i,k{\geq}1$

A SUPPLEMENT TO PRECISE ASYMPTOTICS IN THE LAW OF THE ITERATED LOGARITHM FOR SELF-NORMALIZED SUMS

  • Hwang, Kyo-Shin
    • Journal of the Korean Mathematical Society
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    • v.45 no.6
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    • pp.1601-1611
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    • 2008
  • Let X, $X_1$, $X_2$, ... be i.i.d. random variables with zero means, variance one, and set $S_n\;=\;{\sum}^n_{i=1}\;X_i$, $n\;{\geq}\;1$. Gut and $Sp{\check{a}}taru$ [3] established the precise asymptotics in the law of the iterated logarithm and Li, Nguyen and Rosalsky [7] generalized their result under minimal conditions. If P($|S_n|\;{\geq}\;{\varepsilon}{\sqrt{2n\;{\log}\;{\log}\;n}}$) is replaced by E{$|S_n|/{\sqrt{n}}-{\varepsilon}{\sqrt{2\;{\log}\;{\log}\;n}$}+ in their results, the new one is called the moment version of precise asymptotics in the law of the iterated logarithm. We establish such a result for self-normalized sums, when X belongs to the domain of attraction of the normal law.

Activation Energy Asymptotics Revisited (I);Quasisteady Extinction conidtion of Diffusion Flames (활성화에너지점근법의 재고찰 (I);확산화염의 준정상소화조건)

  • Kim, Jong-Soo
    • 한국연소학회:학술대회논문집
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    • pp.124-132
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    • 2004
  • Activation energy asymptotics (AEA) for Linan's diffusion-flame regime is revisited in this paper. The main purpose of the paper is to carefully re-examine each AEA analysis step in order to clarify the some concepts that are often misunderstood among the ordinary practitioners of the AEA. Particular attention is focused on the different AEA regimes arising from the double limit of large Zel'dovich and Damkohler numbers. In addition. the expansion procedures are shown in detail and the method that the turning point condition, commonly known as the Linan's extinction condition, is found is explained.

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Activation Energy Asymptotics Revisited (I) - Quasisteady Extinction Conidtion of Diffusion Flames (활성화에너지점근법의 재고찰(I) - 확산화염의 준정상소화조건)

  • Kim, Jong-Soo
    • Journal of the Korean Society of Combustion
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    • v.9 no.2
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    • pp.1-9
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    • 2004
  • Activation energy asymptotics (AEA) for Linan#s diffusion-flame regime is revisited in this paper. The main purpose of the paper is to carefully re-examine each AEA analysis step in order to clarify the some concepts that are often misunderstood among the ordinary practitioners of the AEA. Particular attention is focused on the different AEA regimes arising from the double limit of large Zel#dovich and Damkohler numbers. In addition, the expansion procedures are shown in detail and the method that the turning point condition, commonly known as the Linan#s extinction condition, is found is explained.

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Activation Energy Asymptotics Revisited (II) - Diffusion-Flame Structure in the Premixed-Flame Regime (활성화에너지점근법의 재고찰 (II) - 예혼합화염영역에서 확산화염구조)

  • Kim, Jong-Soo
    • Journal of the Korean Society of Combustion
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    • v.9 no.4
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    • pp.35-46
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    • 2004
  • Activation energy asymptotics (AEA) for Linan#s premixed-flame regime is revisited in this paper. First, the detailed AEA procedure for the premixed-flame regime is demonstrated, so that the practitioners of AEA could easily apply the method to their own problems. In addition, the controversies surrounding the premixed-flame regime, namely the closure controversy and fast-time instability paradox, are explained. Finally, the limitation of AEA, mainly arising from the wrong prediction of fuel leakage through the reaction zone, is examined and the Zel#dovich-Linan kinetics is introduced as an alternative to meet the needs of modern combustion analysis, where the detailed chemical structure of flame is demanded.

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PRECISE ASYMPTOTICS IN STRONG LIMIT THEOREMS FOR NEGATIVELY ASSOCIATED RANDOM FIELDS

  • Ryu, Dae-Hee
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.1025-1034
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    • 2010
  • Let {$X_n$, $n\;{\in}\;\mathbb{Z}_+^d$} be a field of identically distributed and negatively associated random variables with mean zero and set $S_n\;=\;{\sum}_{k{\leq}n}\;X_k$, $n\;{\in}\;\mathbb{Z}_+^d$, $d\;{\geq}\;2$. We investigate precise asymptotics for ${\sum}_n|n|^{r/p-2}P(|S_n|\;{\geq}\;{\epsilon}|n|^{1/p}$ and ${\sum}_n\;\frac{(\log\;|n|)^{\delta}}{|n|}P(|S_n|\;{\geq}\;{\epsilon}\;\sqrt{|n|\log|n|)}$, ($0\;{\leq}\;{\delta}\;{\leq}\;1$) as ${\epsilon}{\searrow}0$.

ON PRECISE ASYMPTOTICS IN THE LAW OF LARGE NUMBERS OF ASSOCIATED RANDOM VARIABLES

  • Baek, Jong-Il;Seo, Hye-Young;Lee, Gil-Hwan
    • Honam Mathematical Journal
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    • v.30 no.1
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    • pp.9-20
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    • 2008
  • Let ${X_i{\mid}i{\geq}1}$ be a strictly stationary sequence of associated random variables with mean zero and let ${\sigma}^2=EX_1^2+2\sum\limits_{j=2}^\infty{EX_1}{X_j}$ with 0 < ${\sigma}^2$ < ${\infty}$. Set $S_n={\sum\limits^n_{i=1}^\{X_i}$, the precise asymptotics for ${\varepsilon}^{{\frac{2(r-p)}{2-p}}-1}\sum\limits_{n{\geq}1}n^{{\frac{r}{p}}-{\frac{1}{p}}+{\frac{1}{2}}}P({\mid}S_n{\mid}{\geq}{\varepsilon}n^{{\frac{1}{p}}})$,${\varepsilon}^2\sum\limits_{n{\geq}3}{\frac{1}{nlogn}}p({\mid}Sn{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ and ${\varepsilon}^{2{\delta}+2}\sum\limits_{n{\geq}1}{\frac{(loglogn)^{\delta}}{nlogn}}p({\mid}S_n{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ as ${\varepsilon}{\searrow}0$ are established under the suitable conditions.

ASYMPTOTICS FOR SOLUTIONS OF THE GINZBURG-LANDAU EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

  • Han, Jong-Min
    • Journal of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.1019-1043
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    • 1998
  • In this paper we study some asymptotics for solutions of the Ginzburg-Landau equations with Dirichlet boundary conditions. We consider the solutions ( $u_{\in}$, $A_{\in}$) which minimize the Ginzburg-Landau energy functional $E_{\in}$(u, A). We show that the solutions ( $u_{\in$}$ , $A_{\in}$) converge to some ( $u_{*}$, $A_{*}$) in various norms as the coupling parameter $\in$longrightarrow0.ow0.

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