Gaussian white noise processes

The dWi are Gaussian white noise processes, and their strength a is related to the kinetic friction y through the fluctuation-dissipation relation.72 When deriving integrators for these methods, one has to be careful to take into account the special character of the random forces employed in these simulations.73 A variant of the velocity Verlet method, including a stochastic dynamics treatment of constraints, can be found in Ref. 74. The stochastic... 

The response of a class of elastic shear beam structures subjected to earthquake excitation is studied. The accelerogram of the ground is represented by a nonstationary shaped Gaussian white noise process. The general expressions for the evolutionary power spectra and the mean-square responses of the deflection fleld are developed. The time variations of the response power spectra and the mean-square responses are evaluated and the effects of nonuniformity are discussed. 

When F(t) arises as a vector of Gaussian white noise process or as a vector of filtered white noise processes, it becomes advantageous to interpret Eq. 1 as an Ito s stochastic differential equation (SDE) and represent it as... 

The physical inconsistency on the evaluation of the geometric GSMs, in the nonstationary case, as the moments of the one-sided EPSD function was pointed out by Corotis et al. (1972). In fact they discovered that for the case of the transient response of an oscillator subjected to stationary Gaussian white noise processes, the second GSM does not exist because it is unbounded. At same time in the stationary case, this GSM, which is the limit of the transient as the time approaches infinity, is finite. The first that considered the problem of spectral characteristics from a nongeometric point of view was Di Paola (1985). The basic idea... 

The mean values of the. (t) are zero and each is assumed to be stationary Gaussian white noise. The linearity of these equations guarantees that the random process described by the a. is also a stationary Gaussian-... 

Remark. The white noise limit is not sufficiently defined by just saying rc 0. We have to construct a sequence of processes which in this limit reduce to Gaussian white noise. For that purpose take a long time interval (0, T) and a Poisson distribution of time points Ta in it with density v. To each Ta attach a random number ca they are independent and identically distributed, with zero mean. Consider the process... 

Thus, since the fractional-difference dynamics are linear, the system response is Gaussian, the same as the statistics for the white noise process on the right-hand side of Eq. (22). However, whereas the spectrum of fluctuations is flat, since it is white noise, the spectrum of the system response is inverse power law. From these analytic results we conclude that Xj is analogous to fractional Brownian motion. The analogy is complete if we set a = // 1/2 so that the... 

The integral over the Gaussian white noise gives the Wiener process which stands for the trajectory of a Brownian particle. The integral during... 

The continuous wavelet spectra of paradigmatic processes as Gaussian white noise [8] or fractional Gaussian noise [10] have been studied. The method has been applied to various real world problems of physics, climatology [6], life sciences [5] and other fields of research. Hudgins et. al. [9] defined the wavelet cross spectrum to investigate scale and time dependent linear relations between different processes. This measure found its application e.g. in atmospheric turbulence [9], the analysis of time varying relations between El Nino/Southern Oscillation and the Indian monsoon [20] as well as interrelations of business cycles from different national economies [3]. 

The prediction error is modeled as a discrete zero-mean Gaussian white noise vector process , with e R °, and it satisfies the following correlation structure ... 

Assuming that A and B are rapidly fluctuating quantities, the idealisation of white noise can be adopted, and ft might be considered as a stationary stochastic process, in particular Gaussian white noise with expectation 0 and variance For the associated stochastic process X, the following Ito SDE can be derived ... 

The system mechanical parameters involved are coj = / kT/tm), cos = y/(ks/fns), It = (ct= cs/2y/msks), /u= and So is the Gaussian zero mean white noise process whose intensities, cof and are the base filter frequency and damping. 

Disturbance signal (e,) This represents the unmodelled changes in the process. The disturbance signal is often assumed to be a Gaussian, white noise signal with zero mean and variance... 

It is a very irregular process with no memory at all. As indicated by the fact that its correlation function is a Dirac delta function, i.e. a generalized function, Gaussian white noise is a generalized stochastic process. The use of generalized... 

---