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Explore recent advancements in control theory for stochastic distributed parameter systems in this 45-minute lecture presented at the International Mathematical Union. Delve into the challenges faced when applying deterministic methods to stochastic settings and discover new mathematical tools developed to address these issues. Examine the stochastic transposition method and stochastic Carleman estimate, and their applications to simple stochastic distributed parameter control systems. Focus on recent work regarding controllability for stochastic hyperbolic equations and the Pontryagin-type maximum principle for controlled stochastic evolution equations. Gain insights into new phenomena, difficulties, and methodologies in this evolving field of mathematical control theory.
