Girsanov’s theorem in vector lattices
Abstract
In 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 case
URI
http://hdl.handle.net/10394/31897https://link.springer.com/article/10.1007/s11117-019-00649-5
https://doi.org/10.1007/s11117-019-00649-5