• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.707-723
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• 1996

We first define the concept of the generalized analytic Fourier-Feynman transforms of a class of functionals on function space induced by a generalized Brownian motion process and study of functionals which plays on important role in physical problem of the form $ F(x) = {\int^{T}_{0} f(t, x(t))dt} $ where f is a complex-valued function on $[0, T] \times R$. We next show that the generalized analytic Fourier-Feynman transform of the convolution product is a product of generalized analytic Fourier-Feynman transform of functionals on functin space.

• Journal of Mechanical Science and Technology
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• v.15 no.12
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• pp.1683-1690
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• 2001

A Lagrangian stochastic model is adopted for the calculations of turbulent dispersion in turbulent channel flows. Dispersion of a fluid particle and relative dispersion between two particles released at the sane location are investigated and compared with the classical seating relations for homogeneous turbulence. The viscous effect is realized by adding a Browinian random walk to the calculation of the position of a particle. The near-wall accumulation of particles is examined.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.1-10
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• 2015

This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields. The aim of the present work is to derive explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance studied by Nourdin et al. [Ann. Inst. H. Poincar$\acute{e}$(B) Probab.Statist. 46(1) (2010) 45-98].

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.347-361
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• 2009

In this paper, by estimating small ball probabilities of $l^{\infty}$-valued Gaussian processes, we investigate Chung-type law of the iterated logarithm of $l^{\infty}$-valued Gaussian processes. As an application, the Chung-type law of the iterated logarithm of $l^{\infty}$-valued fractional Brownian motion is established.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.607-625
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• 2013

It is well-known that the ordinary single-parameter Wiener space exhibits a reflection principle. In this paper we establish a reflection principle for a generalized one-parameter Wiener space and apply it to the integration of a class of functionals on this space. We also discuss several notions of a reflection principle for the two-parameter Wiener space, and explore whether these actually hold.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.153-158
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• 2005

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will derive explicit pricing formulas for these floating-strike lookback options with flexible monitoring periods. The monitoring periods of these options start at an arbitrary date and end at another arbitrary date before maturity.

• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.229-236
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• 2011

A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general L$\'{e}$vy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential ${\alpha}$-mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.

• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.1-11
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• 2020

In this paper we determine conditions which a function a(t) must satisfy to insure that the function a'(t) is an element of the separable Hilbert space L²_a,b[0, T]. We then proceed to illustrate our results with several pertinent examples and counter-examples.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.47-60
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• 1997

In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1305-1314
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• 2010

In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations driven by a Brownian motion and the martingales of Teugels associated with an independent L$\acute{e}$vy process having a stochastic Lipschitz coefficient. We derive the existence and uniqueness of solutions for these equations via Snell envelope and the fixed point theorem.