• 재무관리연구
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• 제25권1호
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• pp.85-108
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• 2008

본 연구는 Bender(2003), Duncan et al.(2000)등의 Wick 적분을 이용하여, fBm을 이자율모형의 불확실성으로 사용하였다. Affine 모형에 대표적인 CIR, Hull and White 모형, Quadratic 모형, 그리고 HJM 모형에 차례로 적용한 결과 이론적으로 새로운 결과를 얻었으며, 특히 새로운 확률측도(probability measure)를 정의하여, 할인채권의 옵션가격을 제시하였다.

• 대한수학회보
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• 제57권3호
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• pp.547-568
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• 2020

In this paper, we introduce the linear self-attracting diffusion driven by a weighted fractional Brownian motion with weighting exponent a > -1 and Hurst index |b| < a + 1, 0 < b < 1, which is analogous to the linear fractional self-attracting diffusion. For the 1-dimensional process we study its convergence and the corresponding weighted local time. As a related problem, we also obtain the renormalized intersection local time exists in L² if max{a₁ + b₁, a₂ + b₂} < 0.

• Journal of Applied and Pure Mathematics
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• 제4권1_2호
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• pp.9-26
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• 2022

The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

• 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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• 제38권4호
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• pp.1141-1151
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• 2023

Let C_a,b[0, T] denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier-Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space C_a,b[0, T]. For our purpose, we use the exponential type functions on the general Wiener space C_a,b[0, T]. The class of all exponential type functions is a fundamental set in L₂(C_a,b[0, T]).

• Computers and Concrete
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• 제30권2호
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• pp.143-150
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• 2022

In this paper, the non-linear mathematical problem is solved via numerical scheme by utilizing shooting method. Brownian diffusion and thermophoresis along mass and heat transfer are accounted for. Non-linear expression is reduced via non-dimensional variables. The simplified ordinary differential equations are tackled by shooting technique. Behavior of distinct influential parameters is investigated graphically and analyzed for temperature and concentration profile. Our finding indicates that temperature profile is enhanced for the thermophoresis, Brownian motion coefficient, Prandtl number, Eckert number and temperature slip parameter. Comparison of numerical technique with the extant literature is made and an acceptable agreement is attained. Graphs are plotted to examine the influence of these parameters.

• 대한수학회보
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• 제41권1호
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• pp.73-93
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• 2004

In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

• 대한수학회논문집
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• 제24권3호
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• pp.397-413
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• 2009

In this paper, for functionals of a generalized Brownian motion process, we show that the generalized Fourier-Feynman transform of the convolution product is a product of multiple transforms and that the conditional generalized Fourier-Feynman transform of the conditional convolution product is a product of multiple conditional transforms. This allows us to compute the (conditional) transform of the (conditional) convolution product without computing the (conditional) convolution product.

• 응용통계연구
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• 제23권4호
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• pp.621-633
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• 2010

This paper considers a certain expense structure where a vendor of equity-linked investment product will collect its expenses continuously from the investor's account whenever the investment performance exceeds a certain threshold level. Under the Black-Scholes framework, we derive compact convolution formulas for evaluating the total expenses to be collected during the investment period by using the joint Laplace transform of the Brownian motion and its excursion time. We provide numerical examples for illustration.

• 대한수학회논문집
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• 제20권1호
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• pp.135-144
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• 2005

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 that the set of solutions is closed.