芝, 正己 古谷, 士郎 山本, 俊明 佐々木, 功

計量モデルが離散的な有限個のデータから構造と誤差とを分離する過程を通して構成されると考えるならば (統計的誤差処理), これには 〔1〕 データ特性に関するアプリオリな知識に基づいてモデルが的確に構成されること, 〔2〕 想定されるモデルの中から適切なモデルを比較・評価するための客観的基準が提示されること, 〔3〕 得られたモデルによって何らかの予知・予測が可能になること, が不可欠な条件となる。これらのいずれかの条件が不備であれば, そのモデルの有効性は損われる。著者等は, 数値地形データに対して多項式あるいは2重フーリエ級数をモデルとして採用し 〔1〕, 統計的仮説検定によって多項式の次数およびフーリエ級数の有限項の打切り項数を決定し 〔2〕, これらのモデルを通して, クラスター分析に...

Korolyuk, V. S.
Published in
Ukrainian Mathematical Journal

By using a solution of a singular perturbation problem, we obtain sufficient conditions for the stability of a dynamical system with rapid Markov switchings under the condition of exponential stability of the averaged diffusion process.

Gordin, M. I.
Published in
Journal of Mathematical Sciences

Let T be a measure-preserving transformation of a probability space (X, F, μ) and let A be the generator of a μ-symmetric Markov process with state space X. Under the assumption that A is an “eigenvector” for T an extension of T is constructed in terms of A. By means of this extension a version of the central limit theorem is proved via approximati...

Moulki, M. Beylot, A.L. Truffet, L. Becker, M.
Published in
Annals of Operations Research

This paper illustrates an approximate method to evaluate the cell loss probability of an N x F two-stage ATM switch. Traffic is assumed to be "uniform": arrival processes are simple Bernoulli processes, cells are uniformly directed through output ports, at which finite-capacity buffers are placed. The time evolution of the switch is represented by ...

Bisbas, A. Karanikas, C. Proios, G.
Published in
Results in Mathematics

We estimate the Hausdorff dimension of certain Borel sets determined in dyadic expansion by products of r successive digits.

Lapshin, A. L.
Published in
Ukrainian Mathematical Journal

We obtain an equation of optimal filtration for processes of Markov random evolution, which is a solution of systems of linear differential equations with Markov switchings.

Dzhalladova, I. A.
Published in
Ukrainian Mathematical Journal

We investigate a system of linear differential equations with random coefficients that depend on a periodic Markov process.

Bolthausen, E. Sznitman, A.-S.
Published in
Communications in Mathematical Physics

We construct in this work a Markov process which describes a clustering mechanism through which equivalence classes on ℕ are progressively lumped together. This clustering process gives a new description of Ruelle's continuous probability cascades. It also enables to introduce an abstract cavity method, which mimicks certain features of the cavity ...

Bezuglov, D. A. Pomortsev, P. M.
Published in
Measurement Techniques

Based on mathematical techniques of Markov processes, the usefulness of constructing and utilization of a group measure to increase storage reliability of a physical quantity unit under the conditions of metrological autonomy and decrease in economic expenditures for verification (calibration) of individual measuring devices is demonstrated. Utiliz...

Svishchuk, A. V. Lukin, O. E.
Published in
Ukrainian Mathematical Journal

The problem of estimation of a nonobservable component θt for a two-dimensional process (θt, ξt) of random evolution (θt,ξt);xt, 0≤t≤T, is investigated on the basis of observations of ξs. s≤t, where xt is a homogeneous Markov process with infinitesimal operator Q. Applications to stochastic models of a (B,S)-market of securities is described under ...