About Equation (6) in the paper

[ZhaoRunyi]

Hi! I'm reading your paper and really facinated by your idea that controllablity measured in Gramian form equals the trajectory covariance, it expose a promising way to take the reinforcement learning problem as traditional control theory problem.
However, I stacked in your proof on this idea, namely the Eqution (6) shown in the screenshot below in the Supplementary notes 2.1 of your paper. The eqution in red frame confused me as it change product of 2 integral into 1 integral with the integrand simply multiply.

I try to use the Green's theorem to prove it, only to find that the P&Q is too hard to construct.
I am new in the field and I don't konw if it's appropriate to ask question not related to the code through Github Issue, but really can't find another way to contact with you. If this Issue bother you please let me know.
Hope to hear from you soon and best regards!

[GabrielJardimPP]

@ZhaoRunyi I believe this is Ito's isometry, but I am unsure because the notation is nonstandard for Ito processes.