• Bulletin of the Korean Chemical Society
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• 제13권4호
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• pp.398-404
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• 1992

We have investigated the kinetics of diffusion-influenced bimolecular reactions in which one reactant has an internal mode, called the gating mode, that activates or deactivates its reactivity intermittently. The rate law and an expression for the time-dependent rate coefficient have been obtained from the general formalism based on the hierarchy of kinetic equations involving reactant distribution functions. The analytic expression obtained for the steady-state reaction rate constant coincides with the one obtained by Szabo et al., who derived the expression by employing the conventional concentration-gradient approach. For the time-dependent reaction rate coefficient, we obtained for the first time an exact analytic expression in the Laplace domain which was then inverted numerically to give the time-domain results.

• 대한수학회보
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• 제56권6호
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• pp.1467-1483
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• 2019

This paper analyzes a robust optimal reinsurance and investment strategy for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and insists on seeking robust optimal strategies. The AAI's surplus process is assumed to follow a jump-diffusion model, and he is allowed to purchase proportional reinsurance or acquire new business, meanwhile invest his surplus in a risk-free asset and a risky-asset, whose price is described by an Ornstein-Uhlenbeck process. Under the criterion for maximizing the expected exponential utility of terminal wealth, robust optimal strategy and value function are derived by applying the stochastic dynamic programming approach. Serval numerical examples are given to illustrate the impact of model parameters on the robust optimal strategies and the loss utility function from ignoring the model uncertainty.

• 대한수학회논문집
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• 제21권3호
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• pp.543-558
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• 2006

We consider a type of large deviation Principle(LDP) using Freidlin-Wentzell exponential estimates for the solutions to perturbed stochastic differential equations(SDEs) driven by Martingale measure(Gaussian noise). We are using exponential tail estimates and exit probability of a diffusion process. Referring to Freidlin-Wentzell inequality, we want to show another approach to get LDP for the solutions to SDEs.

• Journal of the Korean Data and Information Science Society
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• 제7권1호
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• pp.69-78
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• 1996

Consider a natural model for stochastic flow systems is Brownian motion, which is Brownian motion on the positive real line with constant drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at $x_{0}$. In this paper, we investigate the joint distribution functions and study on the distribution of the first-passage time. Also we find out the distribution of ${\mu}-RBMPx_{0}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권4호
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• pp.211-224
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• 2010

We define some asset models which are useful for portfolio construction in various terms of time. Our asset models are geometric jump-diffusions defined by the solutions of stochastic differential equations which are decomposed by various terms of time basically. We also can study pricing and hedging strategy of options in our models roughly.

• Communications for Statistical Applications and Methods
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• 제21권4호
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• pp.327-334
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• 2014

Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and ${\beta}$-mixing. The central limit theorem for the process is also obtained.

• 대한수학회보
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• 제48권4호
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• pp.839-845
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• 2011

In this paper, we consider the cusum of squares test for the dispersion parameter in stochastic differential equation models. It is shown that the test has a limiting distribution of the sup of a Brownian bridge, unaffected by the drift parameter estimation. A simulation result is provided for illustration.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2013년도 춘계학술발표대회
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• pp.530-533
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• 2013

본 연구에서는 음악연주 정보를 기록하는 SMF (Standard MIDI File) 대한 정보 하이딩을 스테가노그래피의 관점에서 재고 해 보았다. 그 결과 그 중 SMF 데이터 스트림에 메시지를 은닉 하는 방법이 주로 이용되어 왔다. 연주 정보 통제 방법은 포함할 수 정보량의 증대가 어렵다는 문제가 있었다. 이 보고서는 기존 방식과는 다른 성분인 듀레이션의 확률적 확산을 이용해 정보를 은닉하는 SMF 스테가노그래피를 제안한다.

• 천문학회보
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• 제42권2호
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• pp.37.1-37.1
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• 2017

Since the seminal work of Perrin, physicists have understood in the context of kinetic theory how ink slowly diffuses in a glass of water. The fluctuations of the stochastic forces acting on water molecules drive the diffusion of the ink in the fluid. This is the archetype of a process described by the so-called fluctuation-dissipation theorem, which universally relates the rate of diffusion to the power spectrum of the fluctuating forces. For stars in galaxies, a similar process occurs but with two significant differences, due to the long-range nature of the gravitational interaction: (i) for the diffusion to be effective, stars need to resonate, i.e. present commensurable frequencies, otherwise they only follow the orbit imposed by their mean field; (ii) the amplitudes of the induced fluctuating forces are significantly boosted by collective effects, i.e. by the fact that, because of self-gravity, each star generates a wake in its neighbours. In the expanding universe, an overdense perturbation passing a critical threshold will collapse onto itself and, through violent relaxation and mergers, rapidly converge towards a stationary, phase-mixed and highly symmetric state, with a partially frozen orbital structure. The object is then locked in a quasi-stationary state imposed by its mean gravitational field. Of particular interests are strongly responsive colder systems which, given time and kicks, find the opportunity to significantly reshuffle their orbital structure towards more likely configurations. This presentation aims to explain this long-term reshuffling called gravity-driven secular evolution on cosmic timescales, described by extended kinetic theory. I will illustrate this with radial migration, disc thickening and the stellar cluster in the galactic centre.

• 대한수학회보
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• 제54권4호
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• pp.1195-1219
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• 2017

In this paper, the limit behavior of solution for the $Schr{\ddot{o}}dinger$ equation with random dispersion and time-dependent nonlinear loss/gain: $idu+{\frac{1}{{\varepsilon}}}m({\frac{t}{{\varepsilon}^2}}){\partial}_{xx}udt+{\mid}u{\mid}^{2{\sigma}}udt+i{\varepsilon}a(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic $Schr{\ddot{o}}dinger$ equation with white noise dispersion and time-dependent loss/gain: $idu+{\Delta}u{\circ}d{\beta}+{\mid}u{\mid}^{2{\sigma}}udt+ia(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as ${\varepsilon}{\rightarrow}0$ in one-dimensional $L^2$ subcritical and critical cases.