@Xi'an, I think it's actually just a difference in sign conventions. In the version of the paper that I can find (core.ac.uk/download/pdf/188707037.pdf), the product $v_t \alpha_t$ appears with a minus sign in the exponential (see eq. (45)), whereas in the derivation on Cross Validated the minus sign is missing. FWIW, I prefer the convention in George's answer since it leads to positive $v_t$'s.