SIAM Journal on Control and Optimization, Volume 58, Issue 3, Page 1676-1699, January 2020.
We study a class of nonlinear integrodifferential equations on a subspace of all probability measures on the real line related to the optimal control of McKean--Vlasov jump-diffusions. We develop an intrinsic notion of viscosity solutions that does not rely on the lifting to a Hilbert space and prove a comparison theorem for these solutions. We also show that the value function is the unique viscosity solution.

中文翻译：

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受控McKean-Vlasov跳跃扩散的粘度解决方案

SIAM控制与优化杂志，第58卷，第3期，第1676-1699页，2020年1月。
我们在与McKean-Vlasov最优控制有关的实线上所有概率测度的子空间上研究了一类非线性积分微分方程跳跃扩散。我们提出了不依赖于提升到希尔伯特空间的粘性解决方案的内在概念，并证明了这些解决方案的比较定理。我们还表明，值函数是唯一的粘度解决方案。