• 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.

• 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.

• 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 ${\mathbb{E}}_0$.

• 응용통계연구
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• 제19권3호
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• pp.579-585
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• 2006

본 연구에서는 보험 상품의 잉여금 변화가 브라운 운동을 따르는 파산 모형에 대하여 연구하였다. 만약 잉여금이 재투자를 위한 목표 잉여금을 닿으면 보험회사는 다른 금융 상품에 재투자하는 것으로 가정하였다. 잉여금 과정에 마팅게일 방법을 적용하여 잉여금이 V > 0 또는 0에 도달할 때까지의 시간 T를 초기 잉여금 x(0 < x < V)의 함수로 표시하였으며, 미분방정식을 이용하여 기간 동안의 총 잉여금과 평균 잉여금을 계산하였다.

• 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.

• 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.

• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• 대한수학회보
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• 제40권3호
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• pp.437-456
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• 2003

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra $S(L^2_{a,b}[0,T])$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.