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61.
Sandro Faetti Leone Fronzoni Paolo Grigolini Riccardo Mannella 《Journal of statistical physics》1988,52(3-4):951-978
It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation
1 and an unperturbed part
0. The standard Fokker-Planck structure is recovered at the second order in
1, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in
1 the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in
1, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in
1 vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in
1 vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation. 相似文献
62.
以生命和表面催化体系为对象,研究了介观化学体系中内涨落对体系非线性动力学行为的调控作用。内涨落可以诱导随机振荡,其强度在体系处于最佳尺度时会出现一个甚至多个极大值,并且在耦合体系中会得到进一步增强,表现为尺度共振效应、尺度选择效应和双重尺度效应,揭示了介观化学体系中尺度效应的新机制。 相似文献
63.
The digital filter described provides optimal enhancement of the signal-to-noise ratio by using prior information about peak shape and type of noise. The filter, based onthe matched-filter principle, is applied to chromatographic data, but is also suitable for optimal processing of similar noisy signals. The current implementation of the filter permits the specific reduction of different types of noise. Several theoretical aspects concerning the interpretation and use of this advanced filter are discussed. Some calculations on peaks with Gaussian and Gamma distribution shape are given. 相似文献
64.
本文提出了一种由神经元网络与线性自适应滤波器组成的集成滤波器的实现方法,用于谱图信号除噪处理。 相似文献
65.
Takashi Tateno Shinji Doi Shunsuke Sato Luigi M. Ricciardi 《Journal of statistical physics》1995,78(3-4):917-935
Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator. 相似文献
66.
The principles underlying a novel method intended for analyzing experimental data obtained when studying fluctuation processes are considered. The method in question is Chebyshev’s spectroscopy. The application of this method allows one to determine statistic characteristics of steady-state electrochemical noise against the background of severe deterministic interference without invoking the procedure of the fitting of the initial data. The potentialities of this novel method, which is intended for treating noise experiment, are demonstrated by examining model examples and analyzing the electrochemical noise generated by a lithium electrode placed in an aprotic organic electrolyte. 相似文献
67.
68.
Y. Yavin 《Journal of Optimization Theory and Applications》1984,44(1):159-179
Consider the random motion in the plane of a pointM, whose velocityv=(v
1,v
2) is perturbed by an 2-valued Gaussian white noise. Only noisy nonlinear observations taken on the point location (state) are available toM. The velocityv is of the formv(y)=
u
(u
1,u
2)
y
(du), wherey denotes the value of the observed signal,U is the range of the velocity, and, for eachy,
y
is a probability measure on (U). Using the available observations, the pointM wishes to steer itself into a given target set by choosing a randomized strategy ={
y
:y 2}. Sufficient conditions on weak optimal randomized strategies are derived. An algorithm for computing weak suboptimal randomized strategies is suggested, and the strategies are computed for a variety of cases.This work was partially supported by a grant from Control Data. 相似文献
69.
The paper describes the structure of a new space of generalized Wiener functionals,
, called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process:N
are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of
and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented. 相似文献
70.
N. G. van Kampen 《Journal of statistical physics》1981,25(3):431-442
In the presence of internal noise the variables describing a system are intrinsically stochastic. If they constitute a Markov process the expansion enables one to extract a deterministic macroscopic equation and to compute the fluctuations in successive approximations. In the lowest or linear noise approximation the fluctuations can be represented by a Langevin equation, provided it is handled appropriately. Higher orders cannot be described by any white noise Langevin equation. The question whether the equation has to be interpreted according to Itô or Stratonovich concerns these higher orders, for which the equation is not valid anyway. 相似文献