Probability density of the complex-valued fractional Brownian motion of order \(n\) via the maximum entropy principle in \(\mathbb R_{+}^{1/n}\)
Looking for probability density in the form \(p(z^n)\), where \(n\) is order of the noise, the author couverts an integral over the complex space into the sum of several integrals over the real axis, and from there, to meaningfully extend the definition of informational entropy in this new framework. Then applying the maximum entropy principle will directly yield the sought expression of the complex white noise of order \(n\). The author takes the opportunity to extend the definition of colored noise to obtain the parallel concept of coloured noise of order \(n\) and calculates its (auto)correlation function of order \(n\). As an example of application, the author considers a stability problem in which the equlilibrium position is disturbed by complex-valued noises of order \(n\).
scientific article; zbMATH DE number 2077277
scientific article