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On reconstruction of the Ito-like equation from persistent time series

Czechowski Z.

Acta Geophysica

2013

Vol. 61, no. 6

1504--1521

The Langevin equation with finite-range persistence was introduced as a macroscopic model of various geophysical phenomena. The modified histogram procedure (MHP) of reconstruction of the equation from time series was proposed. An efficiency of MHP was tested on artificial persistent time series (with short and long-tail distributions) generated by different Ito-like equations. For an exemplary geophysical time series, the appropriate Ito-like equation was reconstructed.

On the reconstruction of Ito models on the basis of time series with long-tail distributions

Rozmarynowska A.

Acta Geophysica

2009

Vol. 57, no. 2

311-329

Two methods of reconstruction of Ito equations on the basis of time series were analysed. The Sequin method appeared to be completely inadequate in cases of considerable noise. The histogram method required some improvements; therefore, the procedure of smoothing of joint distribution function was proposed and verified. Ito equations may constitute some macroscopic models of phenomena in which microscopic interactions are averaged in an adequate way. Analysis of two geophysical phenomena is presented. For these two examples, Ito equations are constructed and some physical causes of resulting forms of the deterministic and stochastic force are deduced.

Stochastic approach to movements of a multihull on waves

Królicka A.

Vibrations in Physical Systems

2008

Vol. 23

217--222

Due to difficulties in determining precise initial conditions for the motion of sea waves and the nature of wind undulation, the dynamics of sea waves can be only modelled within the framework of a stochastic theory. The article presents a method for determining differential equations of motion for multihulls, such as catamaran or trimaran. The catamaran sails at constant translatory velocity and at an arbitrary angle to the undulation direction. The set of differential equations of motion presented in the article models anti-symmetric (lateral) movements of the catamaran. For those movements, stochastic differential equations ( Itô equations) are constructed in the form of the equation set (8). Using the state vector X and the excitation vector Y , the Itô equations take the form (9) and (10).