Digital simulation of an arbitrary stationary stochastic process by spectral representation

Digital simulation of an arbitrary stationary stochastic process by spectral representation.

In this paper we present a straightforward, efficient, and computationally fast method for creating a large number of discrete samples with an arbitrary given probability density function and a specified spectral content. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, af...

Spectral Representation of Stationary Processes

The spectral distribution measures the fraction of the total variance of the process γ(0) that can be attributed to a certain interval of frequencies.. If for example we have monthly data then one month corresponds to 2π, two month correspond to π, one year corresponds to π/6 . To measure the fraction of the variance generated by cyclical components of more than one year cycle length we would c...

EXPECTED NUMBER OF CROSSINGS OF AN ARBITRARY CURVE BY A NON-STATIONARY GAUSSIAN PROCESS by

Stochastic Processes ( Fall 2014 ) Spectral representations and ergodic theorems for stationary stochastic processes Stationary stochastic processes

A stochastic process X is strongly stationary if its fdds are invariant under time shifts, that is, for any (finite) n, for any t0 and for all t1, ..., tn ∈ T , (Xt1 , ..., Xtn) and (Xt1+t0 , ..., Xtn+t0) have the same distribution. A stochastic process X is weakly stationary if its mean function is constant and its covariance function is invariant under time shifts. That is, for all t ∈ T , E(...

Mean level signal crossing rate for an arbitrary stochastic process.

The issue of the mean signal level crossing rate for various probability density functions with primary relevance for optics is discussed based on a new analytical method. This method relies on a unique transformation that transforms the probability distribution under investigation into a normal probability distribution, for which the distribution of mean level crossings is known. In general, t...