One-to-one correspondences between discrete multivariate stationary, self-similar and stationary increment fields

2024/01/18 by Voutilainen, Marko · 1 citation
#60G10 #60G18 #60G60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.09909

Abstract

In this article, we consider three important classes of n-variate fields indexed by the set of N dimensional integers, namely stationary, stationary increment and self-similar fields. These classes are connected through bijective transformations. In addition, we introduce generalized AR(1) type equations, whose unique stationary solutions are obtained via these transformations. Lastly, we apply the transformations in order to construct stationary fractional Ornstein-Uhlenbeck fields of the first and second kind.

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• Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration

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