Maximal moments and uniform modulus of continuity for stable random fields

In this work, we provide sharp bounds on the rate of growth of maximal moments for stationary symmetric stable random fields when the underlying nonsingular group action (or its restriction to a suitable lower rank subgroup) has a nontrivial dissipative component. We also investigate the relationship between this rate of growth and the path regularity properties of self-similar stable random fields with stationary increments, and establish uniform modulus of continuity of such fields. In the process, a new notion of weak effective dimension is introduced for stable random fields and is connected to maximal moments and path properties. (C) 2021 Elsevier B.V. All rights reserved.