论文标题
具有Nemytskii-Type系数的McKean-Vlasov SDE的强大解决方案：时间依赖于时间依赖的情况
Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type: the time-dependent case
论文作者
论文摘要
我们根据时间和空间明确考虑具有Nemytskii-type系数的大型非线性FPKE，众所周知，在L^1和l^\ Infty中存在足够的Sobolev期限分布溶液U。我们表明，存在与时间边际密度U的相关McKean-Vlasov SDE的独特强大解决方案。特别是，该方程式的每个弱解决方案都可以用时间边际密度U来写入驱动布朗运动的功能。此外，将任何布朗运动插入这种功能性非常弱的解决方案中，时间边际法律密度U。
We consider a large class of nonlinear FPKEs with coefficients of Nemytskii-type depending explicitly on time and space, for which it is known that there exists a sufficiently Sobolev-regular distributional solution u in L^1 and L^\infty. We show that there exists a unique strong solution to the associated McKean-Vlasov SDE with time marginal law densities u. In particular, every weak solution of this equation with time marginal law densities u can be written as a functional of the driving Brownian motion. Moreover, plugging any Brownian motion into this very functional produces a weak solution with time marginal law densities u.
