• 대한수학회지
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• 제38권3호
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• pp.657-667
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• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.

• 충청수학회지
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• 제25권4호
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• pp.691-701
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• 2012

In this note, we define the It$\hat{o}$ integral with respect to analogue of Wiener process and investigate its various properties and examples.

• 대한수학회보
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• 제40권3호
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• pp.373-383
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• 2003

We investigate a uniform local asymptotic normality for likelihood ratio processes based on an independent and identically distributed local asymptotic problem. Our tool is an empirical process theory.

• 충청수학회지
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• 제12권1호
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• pp.133-146
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• 1999

Let {X(t), $t{\geq}0$} be a stochastic integral process represented by stable random measure or multiple Ito-Wiener integrals. Under some conditions, we prove the continuity and self-similarity of these stochastic integral processes. As an application, we get Gaussian chaos which has some shift continuous function.

• 충청수학회지
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• 제13권2호
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• pp.19-27
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• 2001

In this paper we study another kind of the large deviation property, i.e. moderate deviation type for random amount of random measures on $R^d$ about a Poisson point process and a Poisson center cluster random measure.

• East Asian mathematical journal
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• 제31권3호
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• pp.379-382
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• 2015

The purpose of this note is to study the estimation of errors of the implicit Mann iterative process with random errors.

• 충청수학회지
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• 제5권1호
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• pp.23-34
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• 1992

This is an extension of results of Wiener's nonlinear noise theory from noises generated by the Wiener process to noises generated by processes with stationary Gaussian increments. In particular, using Nisio's Approach, we show that every measurable ergodic noise can be approximated in law by Gaussian process-presentable noise.

• East Asian mathematical journal
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• 제24권3호
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• pp.275-287
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• 2008

In this paper, using large deviation results for Gaussian processes, we establish some functional limit theorems for increments of a fractional Brownian motion in the usual sup-norm via estimating large deviation probabilities for increments of a fractional Brownian motion.

• 충청수학회지
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• 제17권2호
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• pp.197-203
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• 2004

We find some properties of a stochastic processX(t, ${\omega}$) ${\in}L^2_{s.a.p.}$ which is of bounded variation.

• East Asian mathematical journal
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• 제25권1호
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• pp.27-37
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• 2009

In this paper, we introduce an iterative method for a pair of nonexpansive mappings. Strong convergence theorems are established in a real uniformly smooth Banach space.