We find sufficient conditions for convergence of a continuous-time Robbins-Monro type stochastic approximation procedure in infinite dimensional Hilbert spaces in terms of Lyapunova functions, the variational approach to stochastic partial differential equations being used as the main tool.
"A note on continuous-time stochastic approximation in infinite dimensions." Electron. Commun. Probab. 22 1 - 13, 2017. https://doi.org/10.1214/17-ECP67