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

Marko Voutilainen

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arXiv · 2401.09909

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

Marko Voutilainen

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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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Marko Voutilainen. 2024-01-18. One-to-one correspondences between discrete multivariate stationary, self-similar and stationary increment fields. https://arxiv.org/abs/2401.09909

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