Grobler, Jacobus J.Labuschagne, Coenraad C.A.2019-03-052019-03-052019Grobler, J.J. & Labuschagne, C.C.A. 2019. Girsanov’s theorem in vector lattices. Positivity, (In press). [https://doi.org/10.1007/s11117-019-00649-5]1385-12921572-9281 (Online)http://hdl.handle.net/10394/31897https://link.springer.com/article/10.1007/s11117-019-00649-5https://doi.org/10.1007/s11117-019-00649-5In this paper we formulate and proof Girsanov’s theorem in vector lattices. To reach this goal, we develop the theory of cross-variation processes, derive the cross-variation formula and the Kunita–Watanabe inequality. Also needed and derived are properties of exponential processes, Itô’s rule for multi-dimensional processes and the integration by parts formula for martingales. After proving Girsanov’s theorem for the one-dimensional case, we also discuss the multi-dimensional caseenVector latticeRiesz spaceStochastic processBrownian motionItô integralMartingaleGirsanov’s theoremArticle