Boundary-determined maximal regularity conjecture for Gaussian stochastic fields

A Gaussian stochastic field is a stochastic field whose finite-dimensional distributions are Gaussian. Its boundary behaviour means the behaviour of the field when restricted to the boundary of its parameter domain. Boundary regularity conjecture. For a Gaussian stochastic field, the maximal regularity is in general dictated by its behaviour on the boundary. This conjecture suggests that regularity estimates for local times should reflect the regularity of the field on the boundary; the source does not establish sharpness of its regularity results, and the conjecture remains open.