Given two stochastic equations with different drift terms, under very weak
assumptions Liptser and Shiryaev provide the equivalence of the laws of the
solutions to these equations by means of Girsanov transform. Their assumptions
involve both the drift terms. We are interested in the same result but with the
main assumption involving only the difference of the drift terms. Applications
of our result will be presented in the finite as well as in the infinite
dimensional setting.Comment: 22 pages; revised and enlarged versio