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Planar semimartingales obtained by transformations of two-parameter martingales

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Planar semimartingales obtained by transformations of two-parameter martingales SÉMINAIRE DE PROBABILITÉS (STRASBOURG) MINH DUC NGUYEN D. NUALART M. SANZ Planar semimartingales obtained by transformations of two-parameter martingales Séminaire de probabilités (Strasbourg), tome 23 (1989), p. 566-582. <http://www.numdam.org/item?id=SPS_1989__23__566_0> © Springer-Verlag, Berlin Heidelberg New York, 1989, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://www-irma. u-strasbg.fr/irma/semproba/index.shtml), implique l’accord avec les conditions gé- nérales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commer- ciale 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/ PLANAR SEMIMARTINGALES OBTAINED BY TRANSFORMATIONS OF TWO-PARAMETER MARTINGALES By Nguyen Minh Duc*, D. Nualart** and M. Sanz** (*) Institute of Computer Science and Cybemtics Hanoi-Vietnam. (**) Universitat de Barcelona. Barcelona. Spain. Abstract. In this paper we study the weak local submartingale property and the quasimartingale property of processes obtained by the composition of a two-parameter continuous martingale by 2-functions whose second derivative is convex. The work of Nguyen Minh Duc was done during a stay at the University of Barcelona (Spain). 567 0. INTRODUCTION In this paper we are concerned with some properties of the process obtained by the composition of a two-parameter martingale with a 03B62-class function. In the one-parameter case the composition of a martingale with a convex function gives a local submartingale. On the other hand, the semimartingale property is preserved under transformation by convex functions, as can be proved by means of a general version of Tanaka’s formula ([5]). Som

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