• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.129-136
• /
• 2001

We consider a solution process of stochastic differential equation(SDE) driven by S'($R^d$)-valued Wiener process and study a large deviation type of estimates for the process. We get an upper bound in exit probability for such a process to leave a ball of radius $\tau$ before a finite time t. We apply the Ito formula to the SDE under the structure of nuclear space.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.575-583
• /
• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• Journal of the Korean Mathematical Society
• /
• v.41 no.6
• /
• pp.1071-1086
• /
• 2004

This paper is concerned with the strong consistency of the estimators of the autocovariance function and the spectral density function for the autoregressive process in the case where only an amplitude modulated process with missing data is observed. These results will give a simple and practical sufficient condition for the strong consistency of those estimators. Finally, some examples are given to illustrate the application of main result.

• Communications of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.413-422
• /
• 2021

The Study determinant is known as one of replacements for the determinant of matrices with entries in a noncommutative ring. In this paper, we give a generalization of the Study determinant and show its relationship with the Cayley-Dickson process. We also give some properties of a non-associative ring obtained by the Cayley-Dickson process with a not necessarily commutative, but associative ring as the initial ring.

• Journal of the Korean Mathematical Society
• /
• v.61 no.4
• /
• pp.693-711
• /
• 2024

A Markov-modulated Bernoulli process is a generalization of a Bernoulli process in which the success probability evolves over time according to a Markov chain. It has been widely applied in various disciplines for modeling and analysis of systems in random environments. This paper focuses on providing analytical characterizations of the Markovmodulated Bernoulli process by introducing key metrics, including success period, failure period, and cycle. We derive expressions for the distributions and the moments of these metrics in terms of the model parameters.

• The Mathematical Education
• /
• v.44 no.1 s.108
• /
• pp.125-141
• /
• 2005

For many years, the educational effects of instructional manipulatives in mathematics education have been investigated in classroom practice and educational research. This paper demonstrates how pattern block, a type of instructional manipulatives could be used and integrated in elementary mathematics areas in order to develop student's mathematical thinking Further, students' thinking process with pattern blocks is analysed to show their thinking process.

• Macromolecular Research
• /
• v.12 no.2
• /
• pp.206-212
• /
• 2004

To provide guidelines and a basic understanding of static and continuous zone drawing processes, we propose two different mathematical models in terms of the processing conditions and material parameters. Although the models are not finely tuned, because of assumptions made, they are still useful for the analysis of the process and for predicting the processibility.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.63-74
• /
• 2012

Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.

• East Asian mathematical journal
• /
• v.37 no.1
• /
• pp.79-85
• /
• 2021

In this paper, we investigate the valuation of vulnerable exchange option that has credit risk of option issuer. The reduced-form model is used to model credit risk. We assume that credit event is determined by the jump of the counting process with stochastic intensity, which follows the mean reverting process. We propose a simple approach to derive the closed-form pricing formula of vulnerable exchange option under the reduced-form model and provide the pricing formula as the standard normal cumulative function.

• The Mathematical Education
• /
• v.63 no.3
• /
• pp.527-547
• /
• 2024

It is difficult for mathematics teachers to develop mathematical modeling tasks and implement mathematical modeling lessons for their students. These difficulties serve as a reason why mathematical modeling lessons are not implemented well in school mathematics. In this study, we aimed to examine how preservice mathematics teachers (PMTs) modify mathematical modeling tasks in mathematics textbooks as a way to develop mathematical modeling tasks and how they implement the mathematical modeling lesson. In particular, we focused on how the openness and reality reflected in the task and the mathematical modeling process change as PMTs modify the tasks. We collected data through PMTs' evaluation reports on analyzing textbook tasks, task modification, lesson plans and implementations, peer evaluation, and self-evaluation. Then, we analyzed these data according to the case analysis process. The findings revealed that when PMTs modified the textbook task, they focused on and improved the openness and the defining variables and the model stages of mathematical modeling process. However, when PMTs implemented lesson, the openness and the defining variables and the model stages of mathematical modeling process were restricted again. PMTs did not focus on other stages. Based on these results, the theoretical and practical implications of the study was discussed.