• Honam Mathematical Journal
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• v.15 no.1
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• pp.129-136
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• 1993

In this paper we present of a class infinite M A (moving-average) sequences of multivariate random vectors. We use the theory of positive dependence to show that in a variety of cases the classes of M A sequences are associated. We then apply the association to establish some probability bounds and moment inequalities for multivariate processes.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.393-406
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• 2015

We examine how to model mortality risk using the adaptation of the mean-reverting processes for the two factor model proposed by Cairns et al. (2006b). Mortality improvements have been recently observed in some countries such as United Kingdom; therefore, we assume long-run mortality converges towards a trend at some unknown time and the mean-reverting processes could therefore be an appropriate stochastic model. We estimate the parameters of the two-factor model incorporated with mean-reverting processes by a Metropolis-Hastings algorithm to fit United Kingdom mortality data from 1991 to 2015. We forecast the evolution of the mortality from 2014 to 2040 based on the estimation results in order to evaluate the issue price of a longevity bond of 25 years maturity. As an application, we propose a method to quantify the speed of mortality improvement by the average mean reverting times of the processes.

• Water for future
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• v.4 no.1
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• pp.51-58
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• 1971

Hydrologic data serve as an input to the water resources system. An adequate analysis of hydrologic data is one of the most important steps in the planning of the water resources development program. The natural hydrologic processes, which produce the hydrologic data, are truely 'stochastic' in the sense that natural hydrologic phenomena change with time in accordance with the law of probability as well as with sequential relationship between their occurrences. Therefore, the stochastic approach to the analysis of hydrologic data has become more popular in recent years than the conventional deterministic or probabilistic approach. This paper reviews the mathematical models which can adequately simulate the stochastic behavior of the hydrologic characteristics of a hydrologic system. The actual application of these models in the analysis of hydrologic records(precipipitation and runoff records in particular) is also presented.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.543-558
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• 2002

We investigate the fragmentation process developed by Kolmogorov and Filippov, which has been studied extensively by many physicists (independently for some time). One of the most interesting phenomena is the shattering (or disintegration of mass) transition which is considered a counterpart of the well known gelation phenomenon in the coagulation process. Though no masses are subtracted from the system during the break-up process, the total mass decreases in finite time. The occurrence of shattering transition is explained as due to the decomposition of the mass into an infinite number of particles of zero mass. It is known only that shattering phenomena occur for some special types of break-up rates. In this paper, by considering the n-particle system of stochastic fragmentation processes, we find general conditions of the rates which guarantee the occurrence of the shattering transition.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.333-342
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• 2010

The Pseudo-Excitation Method (PEM) is applied to study the stochastic space vibration responses of train-bridge coupling system. Each vehicle is modeled as a four-wheel mass-spring-damper system with two layers of suspension system possessing 15 degrees-of- freedom. The bridge is modeled as a spatial beam element, and the track irregularity is assumed to be a uniform random process. The motion equations of the vehicle system are established based on the d'Alembertian principle, and the motion equations of the bridge system are established based on the Hamilton variational principle. Separate iteration is applied in the solution of equations. Comparisons with the Monte Carlo simulations show the effectiveness and satisfactory accuracy of the proposed method. The PSD of the 3-span simply-supported girder bridge responses, vehicle responses and wheel/rail forces are obtained. Based on the $3{\sigma}$ rule for Gaussian stochastic processes, the maximum responses of the coupling system are suggested.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.4
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• pp.1148-1159
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• 2014

Different procedures for estimation of the extreme global wave hydroelastic responses in ships are discussed. Firstly, stochastic procedures for application in detailed numerical studies (CFD) are outlined. The use of the First Order Reliability Method (FORM) to generate critical wave episodes of short duration, less than 1 minute, with prescribed probability content is discussed for use in extreme response predictions including hydroelastic behaviour and slamming load events. The possibility of combining FORM results with Monte Carlo simulations is discussed for faster but still very accurate estimation of extreme responses. Secondly, stochastic procedures using measured time series of responses as input are considered. The Peak-over-Threshold procedure and the Weibull fitting are applied and discussed for the extreme value predictions including possible corrections for clustering effects.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.23 no.12
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• pp.836-842
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• 2011

It has been shown that the air-conditioning system with slab cooling storage is effective in cutting peak load and utilizing nighttime electric power. The stochastic properties of internal heat generation which has great influence on the cooling load are examined in this paper. Based on the measured cooling load and electric power consumption in an office building with slab cooling storage, stochastic time series models to simulate these random processes are investigated. Furthermore, a calculated result by an optimal control method of thermal analysis taking into account the internal heat is compared with the measured cooling load.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.223-235
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• 2024

In this paper, our primary focus revolves around the examination of a set of fractional stochastic models. Through our investigation, we can establish the presence of a solution and its distinctiveness. Additionally, we employ a moment-based algorithm to estimate the coefficients within these models and provide evidence that these estimations maintain their asymptotic characteristics. To support this claim, we conduct experimental studies using simulations and numerical examples.

• Interdisciplinary Bio Central
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• v.3 no.2
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• pp.8.1-8.6
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• 2011

Background: Thanks to the development of the mathematical/statistical reverse engineering and the high-throughput measuring biotechnology, lots of biologically meaningful genegene interaction networks have been revealed. Steady-state analysis of these systems provides an important clue to understand and to predict the systematic behaviours of the biological system. However, modeling such a complex and large-scale system is one of the challenging difficulties in systems biology. Results: We introduce a new stochastic modeling approach that can describe gene regulatory mechanisms by dividing two (DNA and protein) layers. Simple queuing system is employed to explain the DNA layer and the protein layer is modeled using G-networks which enable us to account for the post-translational protein interactions. Our method is applied to a transcription repression system and an active protein degradation system. The steady-state results suggest that the active protein degradation system is more sensitive but the transcription repression system might be more reliable than the transcription repression system. Conclusions: Our two layer stochastic model successfully describes the long-run behaviour of gene regulatory networks which consist of various mRNA/protein processes. The analytic solution of the G-networks enables us to extend our model to a large-scale system. A more reliable modeling approach could be achieved by cooperating with a real experimental study in synthetic biology.