Arnaudon, Marc Caractéristiques locales des semi-martingales et changements de probabilités. (Local characteristics of semi-martingales and changes of probabilities). (French) Zbl 0736.60043 C. R. Acad. Sci., Paris, Sér. I 313, No. 4, 175-178 (1991). Summary: We write a general Girsanov theorem for manifold-valued semi-martingales using their local characteristics. We compute local characteristics of some Lie group-valued and homogeneous space-valued semi-martingales. This gives conditions on a diffusion \(X\), \(P\)-martingale in a symmetric space of non-compact type \(G/K\), and a path \(g\) in the Lie group \(G\), under which we can find a probability \(Q\) equivalent to \(P\) such that \(g X\) is a \(Q\)-martingale. MSC: 60G48 Generalizations of martingales 58J65 Diffusion processes and stochastic analysis on manifolds 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization Keywords:Girsanov theorem; manifold-valued semi-martingales; Lie group PDF BibTeX XML Cite \textit{M. Arnaudon}, C. R. Acad. Sci., Paris, Sér. I 313, No. 4, 175--178 (1991; Zbl 0736.60043)