• Journal of the Korean Statistical Society
• /
• 제23권2호
• /
• pp.504-512
• /
• 1994

A simple proof for the random central limit theorem is given for a family of stationary linear lattice processes, which belogn to a class of 2 dimensional random fields, applying the Beveridge and Nelson decomposition in time series context. The result is an extension of Fakhre-Zakeri and Fershidi (1993) dealing with the linear process in time series to the case of the linear lattice process with 2 dimensional indices.

• 대한수학회지
• /
• 제58권1호
• /
• pp.237-264
• /
• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• Journal of the Korean Statistical Society
• /
• 제23권2호
• /
• pp.503-503
• /
• 1994

• Korean Chemical Engineering Research
• /
• 제46권3호
• /
• pp.585-597
• /
• 2008

본 연구의 목적은 가동 시간과 생산량에 있어서 무작위 변동을 일으키는 공정 시스템에서 최종 제품의 수요를 만족하는 공정-저장조 망구조의 최적용량을 결정하는 문제의 해석적인 해를 유도하는 것이다. 여기서 논의되는 공장의 구조는 회분식 공정과 저장조가 병렬 또는 직렬로 연결된 망구조를 구성하고 있다. 생산공정은 다수의 원료물질을 다수의 제품으로 일정 비율로 전환한다. 최종제품의 수요는 주문주기와 물량이 무작위 변동을 일으킨다. 일부 생산공정은 생산량에 있어서 무작위 변동을 일으키며, 오염된 물질은 재생공정이나 폐기과정을 거쳐서 처리된다. 다른 공정들은 모두 가동시간이 무작위로 변한다. 최적화의 목적함수는 총비용을 최소화하는 것인데, 여기서 총비용은 준비비와 재고 유지비 그리고 공정과 저장조의 자본비용으로 구성되어 있다. 새로운 생산 재고 분석도구인 사각파 모형은 무작위 흐름의 상한값과 하한값을 계산하는 도형적 방법을 제공한다. 이 모형의 장점은 공정과 저장조 사이의 무작위 흐름을 사실적으로 묘사하면서도 간단한 해석적인 해를 제공하는데 있다. 결과적으로 계산량이 획기적으로 줄어든다.

• 제어로봇시스템학회논문지
• /
• 제16권3호
• /
• pp.305-312
• /
• 2010

The aim of this study is to find an analytic solution to the problem of determining the optimal capacity of a batch-storage network to meet demand for finished products in a system undergoing joint random variations of operating time and batch material loss. The superstructure of the plant considered here consists of a network of serially and/or parallel interlinked batch processes and storage units. The production processes transform a set of feedstock materials into another set of products with constant conversion factors. The final product demand flow is susceptible to joint random variations in the cycle time and batch size. The production processes have also joint random variations in cycle time and product quantity. The spoiled materials are treated through regeneration or waste disposal processes. The objective function of the optimization is minimizing the total cost, which is composed of setup and inventory holding costs as well as the capital costs of constructing processes and storage units. A novel production and inventory analysis the PSW (Periodic Square Wave) model, provides a judicious graphical method to find the upper and lower bounds of random flows. The advantage of this model is that it provides a set of simple analytic solutions while also maintaining a realistic description of the random material flows between processes and storage units; as a consequence of these analytic solutions, the computation burden is significantly reduced. The proposed method has the potential to rapidly provide very useful data on which to base investment decisions during the early plant design stage. It should be of particular use when these decisions must be made in a highly uncertain business environment.

• Journal of the Korean Statistical Society
• /
• 제24권1호
• /
• pp.65-76
• /
• 1995

In this paper, we show that the result of random upper functions for Levy processes obtained by Joo(1993) can be sharpened under some additional assumption. This is the continuous analogue of result obtained by Griffin and Kuelbs (1989) for sums of i.i.d. random varialbles.

• Journal of the Korean Statistical Society
• /
• 제24권1호
• /
• pp.243-248
• /
• 1995

In this article we show that a class of random coefficient autoregressive processes including the NEAR (New exponential autoregressive) process has the strong mixing property in the sense of Rosenblatt with mixing order decaying to zero. The result can be used to construct model free prediction interval for the future observation in the NEAR processes.

• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.299-305
• /
• 2003

The central limit theorems are obtained for stationary linear processes of the form Xt = (equation omitted), where {$\varepsilon$t} is a strictly stationary sequence of random variables which are either linearly positive quad-rant dependent or associated and {aj} is a sequence of .eat numbers with (equation omitted).

• 대한수학회지
• /
• 제35권3호
• /
• pp.583-611
• /
• 1998

We consider a general class of real-valued Levy processes {X(t), $t\geq0$}, and obtain suitable large deviation results for the empiricals L(t, A) defined by $t^{-1}{\int^t}_01_A$(X(s)ds for t > 0 and a Borel subset A of R. These results are used to obtain the asymptotic behavior of P{Z(t) < a}, where Z(t) = $sup_{u\leqt}\midx(u)\mid$ as $t\longrightarrow\infty$, in terms of the rate function in the large deviation principle. A subclass of these processes is the Feller class: there exist nonrandom functions b(t) and a(t) > 0 such that {(X(t) - b(t))/a(t) : t > 0} is stochastically compact, i.e., each sequence has a weakly convergent subsequence with a nondegenerate limit. The stable processes are in this class, but it is much larger. We consider processes in this class for which b(t) may be taken to be zero. For any t > 0, we consider the renormalized process ${X(u\psi(t))/a(\psi(t)),u\geq0}$, where $\psi$(t) = $t(log log t)^{-1}$, and obtain large deviation probability estimates for $L_{t}(A)$ := $(log log t)^{-1}$${\int_{0}}^{loglogt}1_A$$(X(u\psi(t))/a(\psi(t)))dv$. It turns out that the upper and lower bounds are sharp and depend on the entire compact set of limit laws of {X(t)/a(t)}. The results extend to random walks in the Feller class as well. Earlier results of this nature were obtained by Donsker and Varadhan for symmetric stable processes and by Jain for random walks in the domain of attraction of a stable law.

• Journal of applied mathematics & informatics
• /
• 제4권1호
• /
• pp.211-222
• /
• 1997

In this paper we present a probabilistic approach for the estimation of realistic error bounds appearing in the execution of basic algebraic floating point operations. Experimental results are carried out for the extended product the extended sum the inner product of random normalised numbers the product of random normalised ma-trices and the solution of lower triangular systems The ordinary and probabilistic bounds are calculated for all the above processes and gen-erally in all the executed examples the probabilistic bounds are much more realistic.