• 대한수학회지
• /
• 제45권1호
• /
• pp.289-300
• /
• 2008

For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.

• 충청수학회지
• /
• 제4권1호
• /
• pp.121-126
• /
• 1991

In this paper, we show that uniform integrability is equivalent to convergence to a ${\mu}$-integrable function f in $L_1$ for ${\mu}$-integrable functions in the sense of the integral defined by Lewis.

• Journal of the Korean Data and Information Science Society
• /
• 제9권2호
• /
• pp.299-303
• /
• 1998

In this paper weak laws of large numbers are obtained for random variables in $L^{1}(R)$ which satisfy a compact uniform integrability condition.

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.407-415
• /
• 2011

We establish strong laws of large numbers for weighted sums of arrays of negatively associated random variables under the condition of h-integrability and suitable conditions on the array of weights.

• 대한수학회지
• /
• 제49권6호
• /
• pp.1097-1110
• /
• 2012

The convergence properties of extended negatively dependent sequences under some conditions of uniform integrability are studied. Some sufficient conditions of the weak law of large numbers, the $p$-mean convergence and the complete convergence for extended negatively dependent sequences are obtained, which extend and enrich the known results in the literature.

• 대한수학회지
• /
• 제19권2호
• /
• pp.111-116
• /
• 1983

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2003년도 추계 학술발표회 논문집
• /
• pp.183-188
• /
• 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$^{p}$.

• Journal of the Korean Statistical Society
• /
• 제24권2호
• /
• pp.281-292
• /
• 1995

In this paper the concept of strong mixing is extended to random fields, and an invariance principle is obtained for stationary strong mixing random fields.

• Journal of the Korean Statistical Society
• /
• 제22권2호
• /
• pp.353-359
• /
• 1993

In this note we consider other type of tightness than that of Birkel (1988) and prove an invariance principle for nonstationary associated processes by an application of the central limit theorem of Cox and Grimmett (1984), thus avoiding the argument of uniform integrability. This result is an extension to the nonstationary case of an invariance priciple of Newman and Wright (1981) as well as an improvement of the central limit theorem of Cox and Grimmett (1984).

• 대한수학회논문집
• /
• 제12권3호
• /
• pp.779-788
• /
• 1997

In this work, using the exact separatrix map which provides an efficient way to describe dynamics near the separatrix, we study the stochastic layer near the separatrix of a one-degree-of-freedom Hamilitonian system with time periodic perturbation. Applying the twist map theory to the exact separatrix map, T. Ahn, G. I. Kim and S. Kim proved the existence of the uniformly hyperbolic invariant set(UHIS) near separatrix. Using the theorems of Bowen and Franks, we prove this UHIS has measure zero.