Rational dependence of smooth and analytic CR mappings on their jets

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We consider CR submersive mappings between generic submanifolds in complex space. We show that, under suitable conditions on the manifolds, there is an integer k such that any jet of the CR mapping at a given point is a rational function of its k-jet at that point. As a consequence, it is shown that the stability group of a (suitably nondegenerate) real-analytic generic submanifold is a real algebraic Lie group. Moreover, it is shown that a formal equivalence between two such real-analytic submanifolds is necessarily convergent.