• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.419-425
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• 1997

Consider a d-dimensional domain D that has finite Lebesque measure and a Dirichlet form which has discontinuous coefficient. Then the stationary Markov process corresponding to the given Dirichlet form is a semimartingale under suitable condition for D and the coefficient.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.347-358
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• 2009

In [8], the author decomposed the Dirichlet form associated to a bounded generator G of a $weakly^*$-continuous, completely positive, KMS-symmetric Markovian semigroup on a von Neumann algebra M. The aim of this paper is to extend G to the unbounded generator using the bimodule structure and derivations.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.103-110
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• 1995

In their recent paper[2], they show that the existence theory for the analytic operator-valued Feynman path integral can be extended by making use of recent developments in the theory of Dirichlet forms and Markov process. In this field, there is the necessity of studying certain generalized functionals of the process (of Feynman-Kac type). Their study have been concerned with Feynman-Kac type functionals related with smooth measures associated with the classical Dirichlet form (associated with the Laplacian).(omitted)

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.119-130
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• 1995

I study the extension of the definition of the analytic operator-valued Feynman integral to potentials given by a class of signed measures described in terms of additive functionals associated with regular Dirichlet forms.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1797-1803
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• 2015

Let ($S_{\alpha}(n))_{n{\geq}1}$ be the lexicographically greatest Sturmian word of slope ${\alpha}$ > 0. For a fixed ${\sigma}$ > 1, we consider Dirichlet series of the form ${\nu}_{\sigma}({\alpha})$ := ${\Sigma}_{n=1}^{\infty}s_{\alpha}(n)n^{-{\sigma}}$. This paper studies the singular properties of the real function ${\nu}_{\sigma}$, and the Lebesgue-Stieltjes measure whose distribution is given by ${\nu}_{\sigma}$.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.93-117
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• 2019

In this paper we wish to study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of (p, q)-th relative Ritt order, (p, q)-th relative Ritt type and (p, q)-th relative Ritt weak type where p and q are integers such that $p{\geq}0$ and $q{\geq}0$.

• East Asian mathematical journal
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• v.35 no.1
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• pp.67-75
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• 2019

We investigate the averaging value of a random sampling of a Dirichlet series with some condition using Poisson distribution. Our result is the following: Let $L(s)={\sum}^{\infty}_{n=1}{\frac{a_n}{n^s}}$ be a Dirichlet series that converges absolutely for Re(s) > 1. If $X_t$ is an increasing random sampling with Poisson distribution and there exists a number $0<{\alpha}<{\frac{1}{2}}$ such that ${\sum}_{n{\leq}u}a_n{\ll}u^{\alpha}$, then we have $${\mathbb{E}}L(1/2+iX_t)=O(t^{\alpha}{\sqrt{{\log}t}})$$, for all sufficiently large t in ${\mathbb{R}}$. As a result, we get the behaviour of $L({\frac{1}{2}}+it)$ such that L is a Dirichlet L-function or a modular L-function, when t is sampled by the Poisson distribution.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.731-770
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• 1997

We study Diriclet forms and related subjects for the Gibbs measures of classical unbounded sping systems interacting via potentials which are superstable and regular. For any Gibbs measure $\mu$, we construct a Dirichlet form and the associated diffusion process on $L^2(\Omega, d\mu), where \Omega = (R^d)^Z^\nu$. Under appropriate conditions on the potential we show that the Dirichlet operator associated to a Gibbs measure $\mu$ is essentially self-adjoint on the space of smooth bounded cylinder functions. Under the condition of uniform log-concavity, the Gibbs measure exists uniquely and there exists a mass gap in the lower end of the spectrum of the Dirichlet operator. We also show that under the condition of uniform log-concavity, the unique Gibbs measure satisfies the log-Sobolev inequality. We utilize the general scheme of the previous works on the theory in infinite dimensional spaces developed by e.g., Albeverio, Antonjuk, Hoegh-Krohn, Kondratiev, Rockner, and Kusuoka, etc, and also use the equilibrium condition and the regularity of Gibbs measures extensively.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.823-855
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• 1996

We study Dirichlet forms and the associated diffusion processes for the Gibbs measures related to the quantum unbounded spin systems (lattice boson systems) interacting via superstable and regular potentials. This work is a continuation of the author's previous study on the classical systems [LPY] to the quantum cases. In [LPY], we constructed Dirichlet forms and the associated diffusion processes for the Gibbs measures of classical unbounded spin systems. Furthermore, we also showed the essential self-adjointness of the Dirichlet operator and the log-Sobolev inequality for any Gibbs measure under appropriate conditions on the potentials. In this atudy we try to extend the results of the classical systems to the quantum cases. Because of some technical difficulties, we are only able to construct a Dirichlet form and the associated diffusion process for any Gibbs measure of the quantum systems. We utilize the general scheme of the previous work on the theory in infinite dimensional spaces [AH-K1-2, AKR, AR1-2, Kus, MR, Ro, Sch] and the ideas we employed in our study of the calssical systems ]LPY].

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.553-560
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• 2007

In this paper, we consider two components system which lifetimes have Freund's bivariate exponential model with equal failure rates. We propose Bayesian multiple comparisons procedure for the failure rates of I Freund's bivariate exponential populations based on Dirichlet process priors(DPP). The family of DPP is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo(MCMC) method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of multiple comparisons problem for the failure rates of bivariate exponential populations is illustrated through a numerical example.