{'fraction_non_alphanumeric': 0.014804845222072678, 'fraction_numerical': 0.0, 'mean_word_length': 5.888888888888889, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Finding the Most Likely Trajectories of Optimally-Controlled Stochastic Systems

Abstract Optimal trajectories of deterministic systems satisfy Pontryagin's maximum principle and can be computed efficiently. Related results for stochastic systems exist but they lack the simplicity and computational efficiency of the deterministic case. Here we show that a certain class of both discrete-time and continuous-time nonlinear stochastic control problems obey a classic maximum principle, in the sense that the most likely trajectory of the optimally-controlled stochastic system is the solution to a deterministic optimal control problem. Apart from their theoretical significance, our results yield new numerical methods for stochastic control.