| Abstract: |
| This paper studies the most probable transition paths of high dimensional stochastic interacting particle systems and their mean field limits. Since these paths are difficult to compute directly, we reformulate the problem as a mean field optimal control problem based on the Onsager Machlup action functional. Using the stochastic Pontryagin maximum principle, we prove existence and uniqueness of the solution and derive a coupled system for the control variables. We also show that the Hamiltonian extremum conditions are equivalent to the conditions from the Pontryagin maximum principle. This equivalence gives an indirect characterization of the most probable transition paths and shows their correspondence with the paths of the mean field limit system. |
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