• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.513-522
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• 2013

This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.

• 대한산업공학회지
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• 제17권1호
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• pp.117-126
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• 1991

When {X(t), t ${\geq}$ 0} is a Markov process representing time-varying system states, we develop efficient bounding methods for some time-dependent performance measures. We use the discretization technique for stochastically monotone Markov processes and a combination of discretization and uniformization for Markov processes with the stochastic convexity(concavity) property. Sufficient conditions for stochastic monotonocity and stochastic convexity of a Markov process are also mentioned. A simple example is given to demonstrate the validity of the bounding methods.

• 대한수학회보
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• 제40권4호
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• pp.677-683
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• 2003

In multi-allelic model $X\;=\;(x_1,\;x_2,\;\cdots\;,\;x_d),\;M_f(t)\;=\;f(p(t))\;-\;{\int_0}^t\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we examine the stochastic differential equation for model X and find the properties using stochastic differential equation.

• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.111-126
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• 1999

The article is devoted to mathematical modeling of prob-lems of stochastic optimization of the plastic metal working. Classifi-cation and mathematical statements of such problems are proposed. Several calculation techniques of the single goal function are pre-sented. The probability theory and the Fuzzy numbers were applied for solution of the problems of stochastic optimization.

• Journal of the Korean Statistical Society
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• 제31권3호
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• pp.329-342
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• 2002

We deal with asymptotic properties of Maximum Likelihood Estimator(MLE) for the parameters appearing in a Hilbert space-valued Stochastic Differential Equation(SDE) and a Stochastic Partial Differential Equation(SPDE). In paractice, the available data are only the finite dimensional projections to the solution of the equation. Using these data we obtain MLE and consider the asymptotic properties as the dimension of projections increases. In particular we explore a relationship between the conditions for the solution and asymptotic properties of MLE.

• 대한수학회지
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• 제39권4호
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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.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.73-93
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• 2005

In this paper, we attempt to present a new numerical approach to solve non-linear backward stochastic differential equations. First, we present some definitions and theorems to obtain the conditions, from which we can approximate the non-linear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE correspond with the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems, to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original non-linear BSDE in two different cases.

• 대한수학회보
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• 제54권3호
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• pp.917-933
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• 2017

In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

• Korean Journal of Mathematics
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• 제5권1호
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• pp.91-106
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• 1997

The existence and the smoothness of density of random variables which are solutions of the canonical stochastic differential equation can be proved by simpler conditions in the Malliavin-Bismut method.

• Communications for Statistical Applications and Methods
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• 제3권2호
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• pp.187-195
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• 1996

This paper deals with the stochastic comparisons of order statistics from independent but nonidentically distributed (i.n.i.d) variates. And we consider order statistics under positive dependence, negative dependence, and exchangeability.