Fractional Operators and Fractionally Integrated Random Fields on Zν

Autor:	Vytautė Pilipauskaitė, Donatas Surgailis
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	fractional differentiation/integration operators tempered fractional operators fractional random field random walk limit theorems long-range dependence Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 8, Iss 6, p 353 (2024)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract8060353
Popis:	We consider fractional integral operators (I−T)d,d∈(−1,1) acting on functions g:Zν→R,ν≥1, where T is the transition operator of a random walk on Zν. We obtain the sufficient and necessary conditions for the existence, invertibility, and square summability of kernels τ(s;d),s∈Zν of (I−T)d. The asymptotic behavior of τ(s;d) as |s|→∞ is identified following the local limit theorem for random walks. A class of fractionally integrated random fields X on Zν solving the difference equation (I−T)dX=ε with white noise on the right-hand side is discussed and their scaling limits. Several examples, including fractional lattice Laplace and heat operators, are studied in detail.
Databáze:	Directory of Open Access Journals
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