• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.485-490
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• 1998

We consider a class of discrete parameter processes on a locally compact Polish space $S$ arising from successive compositions of strictly stationary Markov random maps on $S$ into itself. Sufficient conditions for the existence of the stationary solution and the weak convergence of the distributions of $\{\Gamma_n \Gamma_{n-1} \cdots \Gamma_0x \}$ are given.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.427-446
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• 1995

Let S be a set and B be a $\sigma$-field on S. We consider $(\Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $\Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = \cdots, X_-1, X_0, X_1, \cdots$ the coordinate maps on $\Omega$. From our assumptions it follows that ${X_i}_{i \in Z}$ is a stationary and ergodic process.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.209-225
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• 1998

In this paper we obtain sharp upper and lower bounds of small ball oprobabilities for Gaussian processes with stationary increments, whose results are essential to estabilish Chung type laws of iterated logarithm.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.509-525
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• 1999

In this paper we obtain sharp upper and lower bounds of samll ball and large deviation probabilities for the increments of Gaussian processes with stationary increments, whose results are essential to establish Chung type laws of iteratted logarithm.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.521-530
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• 1997

The new Laplace autoregressive model of order 2-NLAR92) studied by Dewald and Lewis (1985) is extended to the p-th order model-NLAR(p). A necessary and sufficient condition for the existence of an innovation sequence and a stationary ergodic NLAR(p) model is obtained. It is shown that the distribution of the innovation sequence is given by the probabilistic mixture of independent Laplace distributions and a degenrate distribution.

• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.203-211
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• 2003

A new result of weak convergence of the empirical process is established for a stationary ${\phi}-mixing$ sequence of random variables, which relaxes the existing conditions on mixing coefficients. The result is basically obtained from bounds for even moments of sums of ${\phi}-mixing$ r.v.'s useful for handling triangular arrays with entries decreasing in size.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.117-123
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• 2005

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}= \sum\limits_{j=0}^\infty{a_{j}x_{t-j}}$, where {x_t} is a strictly stationary sequence of negatively associated random variables with suitable conditions and {a_j} is a sequence of real numbers with $\sum\limits_{j=0}^\infty|a_{j}|<\infty$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.63-74
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• 2012

Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.983-990
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• 2006

In this paper, we study an asymmetric power fractionally integrated GARCH model and find a region on which the process is stationary ergodic and has long memory property.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.751-759
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• 2018

Cho et al. (Communications for Statistical Applications and Methods, 23, 423-432, 2016) introduced a risk model with a continuous type investment and studied the stationary distribution of the surplus process. In this paper, we extend the earlier analysis by assuming that additional instant investment is made when the surplus process reaches a certain sufficient level. We obtain the explicit form of the stationary distribution of the surplus process. The case is shown as an example, when the amount of claim is exponentially distributed.