• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.19-32
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• 2005

It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamics dx = (fx + gu)dt + hdb(t, a) where b(t, a) is a fractional Brownian motion of order a, 0 < 2a < 1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments of x(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.

• 대한수학회보
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• 제40권1호
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• pp.159-165
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• 2003

We consider the stochastic differential inclusion of the form $dX_t\;\in\;\sigma(t,\;X_t)db_t+b(t,\;X_t)dt$, where $\sigma$, b are set-valued maps, B is a standard Brownian motion. We prove the boundedness of solutions under the assumption that $\sigma$ and b satisfy the local Lipschitz property and linear growth.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.107-119
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• 2009

In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.179-184
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• 2005

Empirical findings on interet rate dynamics imply that short rates show some long memories and non-Markovin. It is well-known that fractional Brownian motion(fBm) is a proper candidate for modelling this empirical phenomena. fBm, however, is not a semimartingale process. For this reason, it is very hard to apply such processes for asset price modelling. With some modifications, this paper investigate the fBm interest rate theory, and obtain a pure discount bond price and Greeks.

• 충청수학회지
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• 제21권2호
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• pp.231-246
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• 2008

In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

• 대한수학회지
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• 제50권5호
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• pp.1009-1031
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• 2013

In this paper, using elementary calculus only, we give a simple proof that Green function estimates imply the sharp two-sided pointwise estimates for Poisson kernels for subordinate Brownian motions. In particular, by combining the recent result of Kim and Mimica [5], our result provides the sharp two-sided estimates for Poisson kernels for a large class of subordinate Brownian motions including geometric stable processes.

• 대한수학회논문집
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• 제26권4호
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• pp.669-684
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• 2011

In this note, we obtain the expression of the characteristic fucntion of the random variable $\int_o^TB_s^{{\alpha},{\beta}}dB_s^{H,K}$, where $B^{{\alpha},{\beta}}$ and $B^{H,K}$ are two independent bifractional Brownian motions with indices ${\alpha}{\in}(0,1),{\beta}{\in}(0, 1]$ and $HK{\in}(\frac{1}{2},\;1)$ respectively.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.1922-1927
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• 2008

In the present study, deposition of discrete and small particles, which diameter is less than $1{\mu}m$, on a filter element was simulated by stochastic method. Trajectory of each particle was numerically solved by Langevin equation and Brownian random motion was treated by Brownian dynamics. Lattice Boltzmann method (LBM) was used to solve flow field around the filter collector and deposit layer. Interaction between flow field and deposit layer was obtained from a converged solution from an inner-loop calculation. Simulation method is properly validated and collection efficiency due to different filtration parameters are examined and discussed. Morphology of deposit layer and its evolution was visualized in terms of the particle size. The particle loaded effect on collection efficiency was also discussed.

• 대한수학회지
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• 제43권2호
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• pp.357-371
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• 2006

Let $X\;=\;(X_t,\;t{\in}[0, T])$ be a generalized Brownian motion(gBm) determined by mean function a(t) and variance function b(t). Let $L^2({\mu})$ denote the Hilbert space of square integrable functionals of $X\;=\;(X_t - a(t),\; t {in} [0, T])$. In this paper we consider a class of nonlinear functionals of X of the form F(. + a) with $F{in}L^2({\mu})$ and discuss their analysis. Firstly, it is shown that such functionals do not enjoy, in general, the square integrability and Malliavin differentiability. Secondly, we establish regularity conditions on F for which F(.+ a) is in $L^2({\mu})$ and has its Malliavin derivative. Finally we apply these results to compute the price and the hedging portfolio of a contingent claim in our financial market model based on a gBm X.

• 대한수학회지
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• 제36권1호
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• pp.139-157
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• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.