Generalized mixtures of Gaussian processes with an application to Bitcoin daily price analysis

Abstract

In this paper, we apply Rice’s formula, typically employed to calculate the mean number of upcrossings for stationary Gaussian processes, and extend it to the broader framework of generalized mixtures of Gaussian processes. The class of generalized mixtures of Gaussian distributions, recently introduced by [3], is highly comprehensive and includes significant subclasses such as mean mixtures of Gaussian, variance mixtures of Gaussian, meanvariance mixtures of Gaussian, and even scale mixtures of skew-Gaussian distributions. Consequently, our results hold substantial generality, enabling the extension of Rice’s formula to address specific scenarios within these subclasses.

Keywords

• Crossings
• generalized mixture of Gaussian distribution
• Rice’s formula

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