TY - UNPB
T1 - Fractional stable random fields on the Sierpiński gasket
AU - Baudoin, Fabrice
AU - Lacaux, Céline
PY - 2024/1/16
Y1 - 2024/1/16
N2 - We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as (−Δ)−sWK,α, where Δ is the Laplace operator on the gasket and WK,α is a stable random measure. Both Neumann and Dirichlet boundary conditions for Δ are considered. Sample paths regularity and scaling properties are obtained. The techniques we develop are general and extend to the more general setting of the Barlow fractional spaces.
AB - We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as (−Δ)−sWK,α, where Δ is the Laplace operator on the gasket and WK,α is a stable random measure. Both Neumann and Dirichlet boundary conditions for Δ are considered. Sample paths regularity and scaling properties are obtained. The techniques we develop are general and extend to the more general setting of the Barlow fractional spaces.
KW - math.PR
KW - Fractional Riesz kernels
KW - Fractional stable fields
KW - Hölder continuity
UR - http://www.scopus.com/inward/record.url?scp=85205273288&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2024.104481
DO - 10.1016/j.spa.2024.104481
M3 - Preprint
VL - 178
BT - Fractional stable random fields on the Sierpiński gasket
ER -