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On the near-viability property of controlled mean-field flows

  • *Corresponding author: Juan Li

    *Corresponding author: Juan Li
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  • We aim at studying the property of controlled stochastic flows with mean-field dynamics to comply with some (closed) state restrictions. This property, known as (near)-viability, is tackled via (quasi-)tangency methods. Law restrictions and mixed state-law restrictions are considered as the interplay between the two classes. As an auxiliary result used in this process, Theorem 1.2, whose importance exceeds the present framework, dissociates, through a class of elementary controls, the contribution of the Brownian filtration and that of the initial $ \sigma $-field. Explicit conditions for the coefficient functions are provided in the invariance context. Moreover, specific applications to comparison in the convex order illustrate the theoretical results.

    Mathematics Subject Classification: 93E20; 60H10; 60K35.


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