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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