A note on a result of Liptser-Shiryaev

Abstract

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.

22 pages; revised and enlarged version

References in corpus (2)

• SPDEs law equivalence and the compact support property: applications to the Allen-Cahn SPDE
• Uniqueness in Law for the Allen-Cahn SPDE via Change of Measure

Cited by in corpus (1)

• Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift