A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
One-to-one correspondences between discrete multivariate stationary, self-similar, and stationary increment fields
Tekijät: Voutilainen, Marko; Peltonen, Valtteri
Kustantaja: Informa UK Limited
Kustannuspaikka: PHILADELPHIA
Julkaisuvuosi: 2025
Journal: Stochastic Models
Tietokannassa oleva lehden nimi: Stochastic Models
Lehden akronyymi: STOCH MODELS
Sivujen määrä: 34
ISSN: 1532-6349
eISSN: 1532-4214
DOI: https://doi.org/10.1080/15326349.2025.2485116
Verkko-osoite: https://doi.org/10.1080/15326349.2025.2485116
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/491828145
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. We connect these classes through bijective transformations. The one-to-one correspondence between stationary and self-similar fields, where the index of self-similarity is a tuple of positive definite matrices, is given by a version of the Lamperti transformation. In addition, we introduce generalized AR(1) type equations, whose unique stationary solutions are obtained via these transformations. Last, we apply the transformations in order to construct multivariate stationary fractional Ornstein-Uhlenbeck fields of the first and second kind, including a brief simulation study of bivariate Ornstein-Uhlenbeck sheets.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
