• Journal of the Korean Statistical Society
• /
• v.11 no.2
• /
• pp.88-93
• /
• 1982

A local limit theorem for large deviations for the i.i.d. random variables was given by Richter (1957), who used the saddle point method of complex variables to prove it. In this paper we give an alternative form of local limit theorem for large deviations for the i.i.d. random variables which is essentially equivalent to that of Richter. We prove the theorem by more direct and heuristic method under a rather simple condition on the moment generating function (m.g.f.). The theorem is proved without assuming that $E(X_i)=0$.

• Journal of the Korean Statistical Society
• /
• v.13 no.1
• /
• pp.20-24
• /
• 1984

In analogy to the theorem proved by So and Jeon (1982), we give a multi-dimensional version of local limit theorem for large deviations in the continuous case. We also prove a similar theorem in the case of lattice random vectors. Some examples are given.

• Korean Journal of Mathematics
• /
• v.6 no.2
• /
• pp.231-242
• /
• 1998

On the basis of Heyer and Zeuner's results we will treat the central limit theorem for probability measures on hypergroup.

• Journal of the Korean Statistical Society
• /
• v.13 no.2
• /
• pp.81-86
• /
• 1984

Under the i.i.d. hypothesis, authors (1982, 1984) proved some local limit theorems both for the continuous case and for the lattice case. In this paper, results are extended to the case where the random vectors are not identically distributed.

• Journal of the Korean Statistical Society
• /
• v.22 no.2
• /
• pp.307-324
• /
• 1993

The limiting distribution of the excess over the boundary is determined for the autoregressive process.

• The Korean Journal of Applied Statistics
• /
• v.4 no.2
• /
• pp.149-156
• /
• 1991

The theory of the asymptotic behavior of Toeplitz forms is applicable to some problems concerning the local limit theorem.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.855-865
• /
• 1996

In this paper, we establish the weak convergences of processes occurring in a generalized Curie-Weiss model and its dual.

• Journal of the Korean Statistical Society
• /
• v.29 no.1
• /
• pp.1-8
• /
• 2000

A spectrum minimizing the frequency-domain Kullback-Leibler information number has been proposed and used to modify a spectrum estimate. Some numerical examples have illustrated the KL spectrum estimate is superior to the initial estimate, i.e., the autocovariances obtained by the inverse Fourier transformation of the KL spectrum estimate are closer to the sample autocovariances of the given observations than those of the initial spectrum estimate. Also, it has been shown that a Gaussian autoregressive process associated with the KL spectrum is the closest in the timedomain Kullback-Leibler sense to a Gaussian white noise process subject to given autocovariance constraints. In this paper a corresponding conditional probability theorem is presented, which gives another rationale to the KL spectrum.

• Journal of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1483-1504
• /
• 2017

We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain ${\Omega}{\subset}{\mathbb{R}}^3$ with initial value $u_0{\in}L^2_{\sigma}({\Omega})$. It is known that a weak solution is a local strong solution in the sense of Serrin if $u_0$ satisfies the optimal initial value condition $u_0{\in}B^{-1+3/q}_{q,s_q}$ with Serrin exponents $s_q$ > 2, q > 3 such that ${\frac{2}{s_q}}+{\frac{3}{q}}=1$. This result has recently been generalized by the authors to weighted Serrin conditions such that u is contained in the weighted Serrin class ${{\int}_0^T}({\tau}^{\alpha}{\parallel}u({\tau}){\parallel}_q)^s$ $d{\tau}$ < ${\infty}$ with ${\frac{2}{s}}+{\frac{3}{q}}=1-2{\alpha}$, 0 < ${\alpha}$ < ${\frac{1}{2}}$. This regularity is guaranteed if and only if $u_0$ is contained in the Besov space $B^{-1+3/q}_{q,s}$. In this article we consider the limit case of initial values in the Besov space $B^{-1+3/q}_{q,{\infty}}$ and in its subspace ${{\circ}\atop{B}}^{-1+3/q}_{q,{\infty}}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.