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Local time of Reflected Brownian motion in Lipschitz domain with oblique reflection
Kwon, Youngmee 漢城大學校 1998 論文集 Vol.22 No.3
Let (Dn,Vn) n=1,2,..., be smooth domains and smooth reflection vector fields on δDn approximating (D,v), a Lipschitz domain in Rd(d 3) and a given reflection on δD which points uniformly into D. Under the condition that locally for some coordinate system, │vi│<cvd, i=1,...,d, and also the same condition for Vn where c is a constant depending on the Lipschitz constant, it was shown that there is a strong Markov process X on D with reflection v by Kwon. In this paper, we show X is decomposed of Brownian motion and bounded variation.
Convergence of SPDE driven by Gaussian noise
Kwon,Youngmee 漢成大學校 1999 論文集 Vol.23 No.3
We study convergences of solutions of the heat equation with reflection on the spatial interval [0,1] with Dirichlet boundary conditions, driven by an Gaussian noise. The main subject is convergence of the solutions when the related Gaussian noise converge.
Youngmee Kwon,Hye-Jeong Kang 대한수학회 2005 대한수학회지 Vol.42 No.2
An in¯nite system of stochastic di??erential equations(SDE)driven by Brownian motions and compensated Poisson ran-dom measures for the locations and weights of a collection of par-ticles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted mea-sure V , which is shown to be a solution of a stochastic di??erential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.
Reflected Brownian Motion in a Cone: A generalization
Kwon,Youngmee 漢城大學校 1994 論文集 Vol.18 No.1
이 논문에서의 연구대상은 3차원 이상에서의 콘에서 반사하는 브라운 운동이라는 확률과정이다. 특히 경계에서 주어진 반사방향이 접평면에 수직인 성분과 백터길이의 방향의 성분을 제외한 경우 반사하는 방향의 조건에 따라 위의 확률과정의 존재와 유일성이 결정됨은 잘 알려져 있으며 이는 콘과 반사방향으로 결정되는 어떠한 매개변수에 의해 결정된다. 여기서 경계에서의 반사방향이 위의 두성분 이외의 0이 아닌 성분을 가지는 경우에도 이와 같은 결과를 가짐을 보인다. In this paper, the object of study is reflected Brownian motion in a cone in d-dimensions (d≥3) with nonconstant oblique reflection on each redial line emanating from the vertex of the cone. Conditions for the existence anduniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter α-depending on the cone and the direction of reflection when the reflection has only normal and radial components. We extend the results to the reflection with nonzero components other than normal and radial directions.
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS FOR CATALYTIC SUPER-BROWNIAN MOTIONS
Kwon, Youngmee,Kang, Hye-Jeong Korean Mathematical Society 2000 대한수학회보 Vol.37 No.3
We study a class of catalytic super Brownian motion X in 1-dimension. We show under some conditions of catalyst, the process X is absolutely continuous and we get a stochastic partial differential equation for X.
KWON YOUNGMEE,KANG HYE-JEONG Korean Mathematical Society 2005 대한수학회지 Vol.42 No.2
An infinite system of stochastic differential equations (SDE)driven by Brownian motions and compensated Poisson random measures for the locations and weights of a collection of particles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted measure V, which is shown to be a solution of a stochastic differential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.
Kwon, Ji Young,Kim, Youngmee,Kim, Sung-Jin,Lee, Sun Hwa,Kwak, Han,Kim, Cheal Elsevier 2008 Inorganica chimica acta Vol.361 No.7
<P><B>Graphical abstract</B></P><P>Compound <B>1</B> contains [{Ca(phen)(H<SUB>2</SUB>O)<SUB>4</SUB>}{Ca(phen)<SUB>2</SUB>(H<SUB>2</SUB>O)<SUB>3</SUB>}][W<SUB>4</SUB>(μ<SUB>3</SUB>-Te)<SUB>4</SUB>(CN)<SUB>12</SUB>] units bridged by {Ca(phen)<SUB>2</SUB>(H<SUB>2</SUB>O)}<SUP>2+</SUP> units to form an one-dimensional zigzag chain structure. Interestingly, compound <B>1</B> showed a heterogeneous catalytic activity in the transesterification of a range of esters with methanol under the mild conditions. Moreover, it can be reused without any loss of activity through 10 runs with ester.</P><ce:figure></ce:figure> <P><B>Abstract</B></P><P>A new compound containing a cubane tungsten chalcogenide cluster [W<SUB>4</SUB>(μ<SUB>3</SUB>-Te)<SUB>4</SUB>(CN)<SUB>12</SUB>]<SUP>6−</SUP> and Ca<SUP>2+</SUP> complex units has been prepared by the reaction of aqueous solution of K<SUB>6</SUB>[W<SUB>4</SUB>(μ<SUB>3</SUB>-Te)<SUB>4</SUB>(CN)<SUB>12</SUB>]·5H<SUB>2</SUB>O with the solution of a Ca(NO<SUB>3</SUB>)<SUB>2</SUB> and phen(1,10-phenanthroline) (1:2 molar ratio) in a solvent mixture of H<SUB>2</SUB>O/EtOH. The structure of [{Ca(phen)<SUB>2</SUB>(H<SUB>2</SUB>O)}{Ca(phen)(H<SUB>2</SUB>O)<SUB>4</SUB>}{Ca(phen)<SUB>2</SUB>(H<SUB>2</SUB>O)<SUB>3</SUB>}][W<SUB>4</SUB>Te<SUB>4</SUB>(CN)<SUB>12</SUB>]·5H<SUB>2</SUB>O <B>1</B> has been determined by X-ray crystallography. Compound <B>1</B> contains [{Ca(phen)(H<SUB>2</SUB>O)<SUB>4</SUB>}{Ca(phen)<SUB>2</SUB>(H<SUB>2</SUB>O)<SUB>3</SUB>}][W<SUB>4</SUB>(μ<SUB>3</SUB>- Te)<SUB>4</SUB>(CN)<SUB>12</SUB>] units bridged by {Ca(phen)<SUB>2</SUB>(H<SUB>2</SUB>O)}<SUP>2+</SUP> units to form an one-dimensional zigzag chain structure. Interestingly, compound <B>1</B> showed a heterogeneous catalytic activity in the transesterification of a range of esters with methanol under the mild conditions. Moreover, it can be reused without any loss of activity through 10 runs with ester.</P>