Some Families of Random Fields Related to Multiparameter Lévy Processes

Francesco Iafrate and Costantino Ricciuti ()
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Francesco Iafrate: Sapienza University di Roma
Costantino Ricciuti: Sapienza University of Rome

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3055-3088

Abstract: Abstract Let $${\mathbb {R}}^N_+= [0,\infty )^N$$ R + N = [ 0 , ∞ ) N . We here make new contributions concerning a class of random fields $$(X_t)_{t\in {\mathbb {R}}^N_+}$$ ( X t ) t ∈ R + N 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 $$(X_t)_{t\in {\mathbb {R}}^N_+}$$ ( X t ) t ∈ R + N by means of subordinator fields. We finally define the composition of $$(X_t)_{t\in {\mathbb {R}}^N_+}$$ ( X t ) t ∈ R + N 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.

Keywords: Multiparameter Lévy processes; Subordination of random fields; Fractional operators; Semi-Markov processes; Anomalous diffusion; 60G51; 60G60; 60K50 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01351-3

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