| Title |
Fractional operators and fractionally integrated random fields on Zv / |
| Authors |
Pilipauskaitė, Vytautė ; Surgailis, Donatas |
| DOI |
10.3390/fractalfract8060353 |
| Full Text |
|
| Is Part of |
Fractal and fractional.. Basel : MDPI. 2024, vol. 8, iss. 6, art. no. 353, p. [1-20].. eISSN 2504-3110 |
| Keywords [eng] |
conditional autoregression ; fractional differentiation/integration operators ; fractional random field ; limit theorems ; long-range dependence ; negative dependence ; random walk ; tempered fractional operators |
| Abstract [eng] |
We consider fractional integral operators (Formula presented.) acting on functions (Formula presented.), where T is the transition operator of a random walk on (Formula presented.). We obtain the sufficient and necessary conditions for the existence, invertibility, and square summability of kernels (Formula presented.) of (Formula presented.). The asymptotic behavior of (Formula presented.) as (Formula presented.) is identified following the local limit theorem for random walks. A class of fractionally integrated random fields X on (Formula presented.) solving the difference equation (Formula presented.) 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. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2024 |
| CC license |
|
