In his paper On the distributional distance between the Libor and the Swap market models (and also in his book about IR modeling) D.Brigo says:
10, 11, 12 are defined in the end of message. Do I correctly understand that
He simply writes lognormal dynamics in LSM world.
He takes dynamics of forward libors in LFM, translates it to LSM world, expresses Swap rate using these forward rates.
Compares both formulas and finds that it is impossible to derive one from another?
Here are 10,11,12: