  We examine a stochastic Landau-Lifshitz-Gilbert equation based on an exchange
energy functional containing second-order derivatives of the unknown field.
Such regularizations are featured in advanced micromagnetic models recently
introduced in connection with nanoscale topological solitons. We show that, in
contrast to the classical stochastic Landau-Lifshitz-Gilbert equation based on
the Dirichlet energy alone, the regularized equation is solvable in the
stochastically strong sense. As a consequence it preserves the topology of the
initial data, almost surely.
