• Title, Summary, Keyword: strong law

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ON THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF NA RANDOM VARIABLES

  • Kim, T.S.;Ko, M.H.;Lee, Y.M.;Lin, Z.
    • Journal of the Korean Statistical Society
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    • v.33 no.1
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    • pp.99-106
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    • 2004
  • Let {X, $X_{n}, n\;{\geq}\;1$} be a sequence of identically distributed, negatively associated (NA) random variables and assume that $│X│^{r}$, r > 0, has a finite moment generating function. A strong law of large numbers is established for weighted sums of these variables.

ON THE EXPONENTIAL INEQUALITY FOR NEGATIVE DEPENDENT SEQUENCE

  • Kim, Tae-Sung;Kim, Hyun-Chull
    • Communications of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.315-321
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    • 2007
  • We show an exponential inequality for negatively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. To obtain this result we use a truncation technique together with a block decomposition of the sums. We also identify a convergence rate for the strong law of large number.

EXTENSIONS OF SEVERAL CLASSICAL RESULTS FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES TO CONDITIONAL CASES

  • Yuan, De-Mei;Li, Shun-Jing
    • Journal of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.431-445
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    • 2015
  • Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in $L^p$ for conditionally independent and conditionally identically distributed random variables are established, respectively.

ON THE COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF DEPENDENT RANDOM VARIABLES UNDER CONDITION OF WEIGHTED INTEGRABILITY

  • Baek, Jong-Il;Ko, Mi-Hwa;Kim, Tae-Sung
    • Journal of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.1101-1111
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    • 2008
  • Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.

SLIN FOR WEIGHTED SUMS OF STOCHASTICALLY DOMINATED PAIRWISE INDEPENDENT RANDOM VARIABLES

  • Sung, Soo-Hak
    • Communications of the Korean Mathematical Society
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    • v.13 no.2
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    • pp.377-384
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    • 1998
  • Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

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COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF AANA RANDOM VARIABLES AND ITS APPLICATION IN NONPARAMETRIC REGRESSION MODELS

  • Shen, Aiting;Zhang, Yajing
    • Journal of the Korean Mathematical Society
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    • v.58 no.2
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    • pp.327-349
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    • 2021
  • In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.

STRONG CONVERGENCE FOR WEIGHTED SUMS OF FUZZY RANDOM VARIABLES

  • Kim, Yun-Kyong
    • Proceedings of the Korean Statistical Society Conference
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    • pp.183-188
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    • 2003
  • In this paper, we establish some results on strong convergence for weighted sums of uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

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CISG and Arbitration Agreements: A Janus-Faced Practice and How to Cope with It

  • Flecke-Giammarco, Gustav;Grimm, Alexander
    • Journal of Arbitration Studies
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    • v.25 no.3
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    • pp.33-58
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    • 2015
  • Arbitration clauses or institutional arbitration rules rarely, if ever, specify the law applicable to the arbitration agreement. A wide range of laws may thus govern this question, such as the law at the place of arbitration, the law where the agreement or the award is enforced or the law of the main contract between the parties. It is also conceivable that international uniform law or soft law may play a role. Tribunals and courts seized with this question must consequently decide which of these various laws shall apply to verify the existence and validity of the arbitration agreement. This paper picks up on this controversially debated conflict of laws issue. At times, this debate is characterized by a strong divide between arbitration and international trade law practitioners. But are the different approaches really leading to diverging results in arbitral practice?