• 충청수학회지
• /
• 제12권1호
• /
• pp.119-124
• /
• 1999

In this paper, T.Kawata's result[2] is generalized, by means of Hausdorff-Young inequality and Beurling's norm.

• 대한수학회지
• /
• 제38권2호
• /
• pp.311-319
• /
• 2001

We show that it is possible to associate diffusion processes to second order perturbations of the Ornstein-Uhlenbeck operator L on the Wiener space of the form L = L + 1/2∑L$^2$(sub)ξ(sub)$\kappa$ where the ξ(sub)$\kappa$ are "tangent processes" (i.e., semimartingales with antisymmetric diffusion coefficients).

• 대한수학회논문집
• /
• 제25권1호
• /
• pp.119-128
• /
• 2010

Let ${X_n,\;n\geq1}$ be a sequence of independent identically distributed (i.i.d.) random variables (r.vs.), defined on a probability space ($\Omega$,A,P), and let ${N_n,\;n\geq1}$ be a sequence of positive integer-valued r.vs., defined on the same probability space ($\Omega$,A,P). Furthermore, we assume that the r.vs. $N_n$, $n\geq1$ are independent of all r.vs. $X_n$, $n\geq1$. In present paper we are interested in asymptotic behaviors of the random sum $S_{N_n}=X_1+X_2+\cdots+X_{N_n}$, $S_0=0$, where the r.vs. $N_n$, $n\geq1$ obey some defined probability laws. Since the appearance of the Robbins's results in 1948 ([8]), the random sums $S_{N_n}$ have been investigated in the theory probability and stochastic processes for quite some time (see [1], [4], [2], [3], [5]). Recently, the random sum approach is used in some applied problems of stochastic processes, stochastic modeling, random walk, queue theory, theory of network or theory of estimation (see [10], [12]). The main aim of this paper is to establish some results related to the asymptotic behaviors of the random sum $S_{N_n}$, in cases when the $N_n$, $n\geq1$ are assumed to follow concrete probability laws as Poisson, Bernoulli, binomial or geometry.

• Journal of applied mathematics & informatics
• /
• 제8권2호
• /
• pp.519-530
• /
• 2001

A two commodity continuous review inventory system with independent Poisson processes for the demands is considered in this paper. The maximum inventory level for the i-th commodity fixed as $S_i$(i = 1,2). The net inventory level at time t for the i-th commodity is denoted by $I_i(t),\;i\;=\;1,2$. If the total net inventory level $I(t)\;=\;I_1(t)+I_2(t)$ drops to a prefixed level s $[{\leq}\;\frac{({S_1}-2}{2}\;or\;\frac{({S_2}-2}{2}]$, an order will be placed for $(S_{i}-s)$ units of i-th commodity(i=1,2). The probability distribution for inventory level and mean reorders and shortage rates in the steady state are computed. Numerical illustrations of the results are also provided.

• Journal of applied mathematics & informatics
• /
• 제33권5_6호
• /
• pp.607-625
• /
• 2015

Recently, Wang et al. [Computers and Mathematics with Ap-plications 57 (2009) 1232-1248.] and Wang and Watada [Information Sci-ences 179 (2009) 4057-4069.] studied the renewal process and renewal reward process with fuzzy random inter-arrival times and rewards under the T-independence associated with any continuous Archimedean t-norm. But, their main results do not cover the classical theory of the random elementary renewal theorem and random renewal reward theorem when fuzzy random variables degenerate to random variables, and some given assumptions relate to the membership function of the fuzzy variable and the Archimedean t-norm of the results are restrictive. This paper improves the results of Wang and Watada and Wang et al. from a mathematical per-spective. We release some assumptions of the results of Wang and Watada and Wang et al. and completely generalize the classical stochastic renewal theorem and renewal rewards theorem.

• 대한수학회지
• /
• 제33권4호
• /
• pp.777-791
• /
• 1996

Let $S(R^d)$ be the Schwartz space of infinitely differentiable functions on $R^d$ which vanish at $\infty$ and $S'(R^d)$ be its dual space. The theory of stochastic differential equations(SDEs) governing processes that takes values in the dual of countably Hilbertian nuclear space such as $S'(R^d)$ studied by many authors(e.g [M],[KM]). Let M be a martingale measure defined by Walsh[W], then M can be considered as a $S'(R^d)$-valued process in a certain condition i.e. M has a version of $S'(R^d)$-valued martingale process. (See [W] for detailed discussion)

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
• /
• pp.357-357
• /
• 2000

In this study, we consider a multi-input multi-output styrene polymerization reactor system for which the monomer conversion and the weight average molecular weight are controlled by manipulating the jacket inlet temperature and the feed flow rate. The reactor system is identified by using a linear subspace identification method and then the output feedback model predictive controller is constructed on the basis of the identified model. Here we use the Best Linear Unbiased Estimation (BLUE) filter as a stochastic estimator instead of the Kalman filter. The BLUE filter observes the state successfully without any a priori information of initial states. In contrast to the Kalman filter, the BLUE filter eliminates the offset by observing the state of the augmented system regardless of a priori information of the initial state for an integral white noise augmented system. A BLUE filter has a finite impulse response (FIR) structure which utilizes finite measurements and inputs on the most recent time interval [i-N, i] in order to avoid long processing times.

• 한국시뮬레이션학회:학술대회논문집
• /
• 한국시뮬레이션학회 1998년도 추계학술대회 및 정기총회
• /
• pp.65-65
• /
• 1998

Manufacturing systems like a motor production process are analyzed using simulations than numerical analyses and/or heuristic methods due to their stochastic properties. The SME(small and medium enterprise) producing automotive motors that develop CIM systems to improve production performance is focused as an application site. We analyze and understand the system exactly using layout based simulation, and then we will suggest the initial feashible production-plan dependent on the layout to overcome weak-points of the current system(i.e., high WIPs, bottle-neck processes, due-date delays and etc.). And, solutions are suggested to increase performances of SMEs producing automotive motors in this paper. The simulation model built in this study is moedlled and analyzed with fully object-oriented methodology using SiMPLE++TM according to properties of production processes of the automotive motor. And, we will introduce ways to verify the model with developed templates for reusability when new needs will be occurred such as designing a new ship, extension or rearrangement of the system, change of production-plans, receiving urgent orders, and so on.

• 천문학회보
• /
• 제39권2호
• /
• pp.71.2-71.2
• /
• 2014

processes at the origin of the star formation in the galaxies over the last 10 billions years. While it was proposed in the past that merging of galaxies has a dominant role to explain the triggering of the star formation in the distant galaxies having high star formation rates. In the opposite, more recent studies revealed scaling laws linking the star formation rate in the galaxies to their stellar mass or their gas mass. The small dispersion of these laws seems to be in contradiction with the idea of powerful stochastic events due to interactions, but rather in agreement with the new vision of galaxy history where the latter are continuously fed by intergalactic gas. I was especially interested in one of this scaling law, the relation between the star formation (SFR) and the stellar mass (M*) of galaxies, commonly called the main sequence of star forming galaxies. I have studied this main sequence, SFR-M*, in function of the morphology and other physical parameters as the radius, the colour, the clumpiness. The goal was to understand the origin of the sequence's dispersion related to the physical processes underlying this sequence in order to identify the main mode of star formation controlling this sequence. This work needed a multi-wavelength approach as well as the use of galaxies profile simulation to distinguish between the different galaxy morphological types implied in the main sequence.

• 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.