Can stochastic PDE theory be applied to elliptic PDE to get the solvability when it's hard to use traditional prior estimate or flow approach

Question

Recently I'm interested in stochastic PDE on manifold and I knew that for some famous geometry theorems such as Atiyah-Singer index theorem there is proof by stochastic analysis approach, I wonder that for an elliptic PDE, if many researchers have studied it through many ways like variational method, prior estimate, or flow approach, but none of them get good results, will the stochastic pde be a good tool to provide a new way to solve it? Did any researchers have tried like this to prove the existence of solution of elliptic PDE by stochastic analysis method?