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An estimate for fractal dimension of trajectories generated by a multiplicative noise
Nobutoshi Ikeda 한국물리학회 2005 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.46 No.3
Investigations are carried out on trajectories generated by a multiplicative noise in a second order stochastic dierential equation. A way of estimating the fractal dimension is proposed; accordingly, noise-induced transitions can be detected by observing the geometrical structures of the trajectories, such as the fractal dimension. Our approach can make it possible to estimate changes in the properties of a time series with nite length without getting precise information about probability distribution.