Some families of random fields related to multiparameter Lévy processes

Let R+N=[0,∞)N. We here make new contributions concerning a class of random fields (Xt)javax.xml.bind.JAXBElement@17e2af23javax.xml.bind.JAXBElement@232cad15Rjavax.xml.bind.JAXBElement@72133445javax.xml.bind.JAXBElement@3aa07657 which are known as multiparameter Lévy processes. Related multiparameter semigroups of operators and their generators are represented as pseudo-differential operators. We also provide a Phillips formula concerning the composition of (Xt)javax.xml.bind.JAXBElement@38394d97javax.xml.bind.JAXBElement@7e3b1b80Rjavax.xml.bind.JAXBElement@15e1a91ejavax.xml.bind.JAXBElement@2c4a673b by means of subordinator fields. We finally define the composition of (Xt)javax.xml.bind.JAXBElement@5e6dc2d0javax.xml.bind.JAXBElement@78ac3586Rjavax.xml.bind.JAXBElement@609dcad4javax.xml.bind.JAXBElement@1f911a43 by means of the so-called inverse random fields, which gives rise to interesting long-range dependence properties. As a byproduct of our analysis, we present a model of anomalous diffusion in an anisotropic medium which extends the one treated in Beghin et al. (Stoch Proc Appl 130:6364–6387, 2020), by improving some of its shortcomings.