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Caractéristiques locales des semi-martingales et changements de probabilités. (Local characteristics of semi-martingales and changes of probabilities). (French) Zbl 0736.60043
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
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