• Journal of applied mathematics & informatics
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• 제41권5호
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• pp.923-935
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• 2023

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as ^c₀D^𝛼_𝜌 Ψ_𝜌 = 𝒜(𝜌)Ψ_𝜌d𝜌 + 𝚽(𝜌, Ψ_𝜌)d𝜌 + ϒ(𝜌, Ψ_𝜌)d ⟨ℵ⟩_𝜌 + χ(𝜌, Ψ_𝜌)dℵ_𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

• 대한수학회논문집
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• 제11권2호
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• pp.471-480
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• 1996

Consider a strong Markov process $X^0$ that has continuous sample paths in the closed cone $\bar{G}$ in $R^d(d \geq 3)$ such that the process behaves like a ordinary Brownian motion in the interior of the cone, reflects instantaneously from the boundary of the cone and is absorbed at the vertex of the cone. It is shown that $X^0(t)$ has a representation $R(t) \ominus (t)$ where $R(t) \in [0, \infty)$ and $\ominus(t) \in S^{d-1}$, the surface of the unit ball.

• 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.

• 호남수학학술지
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• 제45권3호
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• pp.433-456
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• 2023

This paper deals with differentiability of solutions of neutral stochastic differential equations with respect to the initial data in the G-framework. Since the initial data belongs to the space BC ([-r, 0] ; ℝⁿ) of bounded continuous ℝⁿ-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space 𝓛_BC (ℝⁿ) of linear bounded operators from BC ([-r, 0] ; ℝⁿ) to ℝⁿ. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.

• 대한수학회보
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• 제48권3호
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• pp.475-489
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• 2011

In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form F(x) = $\hat{v}$(($g_1,x)^{\sim}$,..., $(g_n,x)^{\sim}$) defined on a very general function space $C_{a,b}$[0,T]. We also present a change of scale formula for function space integrals of such cylinder functionals.

• Bulletin of the Korean Chemical Society
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• 제19권10호
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• pp.1068-1072
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• 1998

We present results of molecular dynamic (MD) simulations for the segmental motion of liquid n-butane as the base case for a consistent study for conformational transition from one rotational isomeric state to another in long chains of liquid n-alkanes. The behavior of the hazard plots for n-butane obtained from our MD simulations are compared with that for n-butane of Brownian dynamics study. The MD results for the conformational transition of n-butane by a Poisson process form the total first passage times are different from those from the separate t-g and g-t first passage times. This poor agreement is probably due to the failure of the detailed balance between the fractions of trans and gauche. The enhancement of the transitions t-g and g-t at short time regions are also discussed.

• 상하수도학회지
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• 제9권4호
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• pp.63-72
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• 1995

The mean velocity gradient, G, has been used as a principal design and operation parameter for flocculation unit. This paper questions that significance. The physical and qualitative meaning of collision efficiency factors of each transport mechanism (Brownian motion, fluid shear, and differential sedimentation) are reviewed. The overall collision frequency function is calculated by summing up the collision frequency function of each mechanism. In the collision of two particles of different size, a diagram showing the dominant region in which each mechanism is important is developed and the meaning of the diagram is discussed. The primary ramification of this curvilinear, heterodisperse approach is that G is found to be not nearly so important. Previous experimental work in which the role of G has been examined is reviewed in light of this finding.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권1호
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• pp.13-30
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• 2007

In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $$du(x,\;t)\;=\;f(x,\;t,\;u_t)dt\;+\;g(x,\;t,\;u_t)dB(t),\;t\;>\;0$$ with initial data $u(x,\;0)\;=\;u_0(x)\;=\;{\xi}\;{\in}\;L^p_{F_0}\;([-{\tau},0];\;R^n)$. Here $x\;{\in}\;R^n$, ($R^n$ is the ${\nu}\;-\;dimenional$ Euclidean space), $f\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^n,\;g\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^{n{\times}m},\;u(x,\;t)\;{\in}\;R^n$ for each $t,\;u_t\;=\;u(x,\;t\;+\;{\theta})\;:\;-{\tau}\;{\leq}\;{\theta}\;{\leq}\;0\;{\in}\;C([-{\tau},\;0];\;R^n)$, and B(t) is an m-dimensional Brownian motion.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권1호
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• pp.79-90
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• 2005

In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

• 한국산업정보학회논문지
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• 제15권3호
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• pp.51-57
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• 2010

스테가노그래피는 이미지의 외적인 면에서 미세한 변화를 가진 디지털 이미지에 자료를 은닉하기 위해 사용된다. 은닉이미지가 의심되는 스테고 신호 분석에서 개선된 통계량을 이용하여 갑작스러운 변화를 신속, 정확하게 감지하는 기법의 개발이 필요하다. 이 논문에서는 축차적인 스테가노그래피에서 은닉된 메시지를 감지하고 그 위치를 찾아내는 방법을 제시한다. 즉, 검사하는 이미지에 은닉메시지의 존재 유무를 결정하고 그 위치를 찾아낼 때까지 CUSUM-SPRT 스테간 분석을 기반으로 하는 통계적 검정을 반복한다. 논문에서 일반화된 수식을 위해 개선된 $S^{t^*}_j$를 이용한 통계량 $g_t$를 사용한다.