In this article the authors present a method and a scale for the evaluation of the metacognitive profiles of psychotherapy patients. There will be a description of the metacognitive function and of the alterations that occur to it during treatment. Various hypotheses will then be considered: (1) that the metacognitive function has a modular structure; (2) that for each type of psychopathological condition there is a different metacognitive deficit profile; (3) that to be successful psychotherapy needs to involve an improvement in any deficient metacognitive sub-function. There will then be a presentation of the Metacognition Assessment Scale (MAS) for the assessment of metacognitive deficits during psychotherapy. We shall then describe the first results we have on the application of the scale. Finally there will be an analysis of two patients suffering from Personality Disorders and a demonstration of what metacognitive deficit profile each one has and how it is modified over the course of psychotherapy treatment. The article ends with a discussion of the hypotheses made at the start in the light of the results that have emerged.

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An approximation scheme for the optimal control of diffusion processes RAIRO-Modélisation mathématique et analyse numérique, tome 29, n o 1 (1995), p. 97-122. © AFCET, 1995, tous droits réservés. L'accès aux archives de la revue « RAIRO-Modélisation mathématique et analyse numérique » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ fTf^T) MATWMATH^MOOeUJMGAHOWMEWCAlANALYStS l,M/\f j MOOÉUSATIOHMATMÉMATKKJE ET ANALYSE HOMÉRWUC

We are concerned with the Hamilton-Jacobi equation related to the infinite horizon problem of deterministic control theory. Approximate solutions are constructed by means of a discretization in time as well as in the state variable and we prove that their rate of convergence to the viscosity solution is of order 1, provided a semiconcavity assumption is satisfied. A computational algorithm, originally due to R. Gonzales and E. Rofman, is adapted and reformulated for the problem at hand in order to obtain an error estimate for the numerical approximate solutions.