Regularity of Gaussian Fields from Kernel Conditions via Wavelets

In recent years, the study of the (ir)regularity of various stochastic processes
has attracted the attention of several authors. In this
work, we aim to study a large class of Gaussian fields defined via a stochastic integral. More precisely, we seek to obtain a general strategy to deduce sharp regularity and irregularity estimates using wavelet methods. This approach should allow us to recover and compare regularity results appearing in the literature within a unified framework. Key ideas will be presented, along with some preliminary results.