Communications in Information and Systems

Volume 21 (2021)

Number 2

Mean field verification theorem

Pages: 253 – 267



Alain Bensoussan (International Center for Decision and Risk Analysis, University of Texas, Dallas, Tx., U.S.A.; and City University of Hong Kong)

SingRu (Celine) Hoe (Texas A&M University, Commerce, Tx., U.S.A.)

Joohyun Kim (International Center for Decision and Risk Analysis, University of Texas, Dallas, Tx., U.S.A.)

Zhongfeng Yan (Department of Mathematics, Jinan University, Guangzhou, China)


It is well known in deterministic and stochastic control that an optimal control can be obtained through a theory of sufficient conditions, so-called Bellman or Dynamic Programming approach. In Bellman’s approach, one constructs a control under sufficient conditions and proves that this control is optimal by an argument called verification theorem. This presentation aims at describing the basic ideas of the verification theorem for mean field type control theory.


verification theorem, mean field type control, sufficient condition

As originally published in print and online, this article’s title contained a typographical error (‘filed’ for ‘field’). This error has now been corrected, as of 6 July 2021, in the article’s online publication.

Alain Bensoussan is supported by the National Science Foundation under grants DMS-1612880, DMS-1905459.

Zhongfeng Yan is supported by the National Natural Science Foundation of China (Grant Nos. 11601186).

Received 14 September 2020

Published 3 June 2021