Jonas Wallin
Universitetslektor, Studierektor för forskarutbildningen, Statistiska institutionen
Gaussian Whittle–Matérn fields on metric graphs
Författare
Summary, in English
We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle–Matérn fields, are defined via a fractional stochastic differential equation on the compact metric graph and are a natural extension of Gaussian fields with Matérn covariance functions on Euclidean domains to the non-Euclidean metric graph setting. Existence of the processes, as well as some of their main properties, such as sample path regularity are derived. The model class in particular contains differentiable processes. To the best of our knowledge, this is the first construction of a differentiable Gaussian process on general compact metric graphs. Further, we prove an intrinsic property of these processes: that they do not change upon addition or removal of vertices with degree two. Finally, we obtain Karhunen–Loève expansions of the processes, provide numerical experiments, and compare them to Gaussian processes with isotropic covariance functions.
Avdelning/ar
- Statistiska institutionen
Publiceringsår
2024-05
Språk
Engelska
Sidor
1611-1639
Publikation/Tidskrift/Serie
Bernoulli
Volym
30
Issue
2
Dokumenttyp
Artikel i tidskrift
Förlag
Chapman and Hall
Ämne
- Probability Theory and Statistics
Nyckelord
- Gaussian processes
- networks
- quantum graphs
- stochastic partial differential equations
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 1350-7265