Abstract
A model is proposed to, e.g., control the domain wall motion in ferromagnets in the presence of thermal fluctuations, and the existence of an optimal stochastic control process is proved. The convergence of a finite element approximation of the problem is shown in space-dimension one, which then allows one to apply Pontryagin’s maximum principle for this finite dimensional setting. The resulting coupled system of forward-backward stochastic differential equations is numerically solved by means of the stochastic gradient method to enable practical simulations.
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