Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow

arXiv:2610.32588v1 Announce Type: new Abstract: We study the stochastic harmonic map heat flow into the sphere driven by a Stratonovich noise term that formally preserves the spherical constraint by construction. Starting from a fully discrete, implementable numerical scheme, we prove its convergence to the novel solution concept of probabilistically strong, analytically energy-variational solutions. This yields the first existence result for probabilistically strong solutions in the three-dimensional setting on the prescribed stochastic basis. In addition, we establish weak-strong uniqueness and illustrate our theoretical findings with numerical experiments.