Differentiation of Multiparameter Superadditive Processes

Çömez, Doğan

Canadian journal of mathematics, Tome 37 (1985) no. 3, pp. 385-404

Résumé

In this article our purpose is to prove a differentiation theorem for multiparameter processes which are strongly superadditive with respect to a strongly continuous semigroup of positive L 1 contractions (see Section 1 for definitions).Recently, the differentiation theorem for superadditive processes with respect to a one-parameter semigroup of positive L 1-contractions has been proved by D. Feyel [9]. Another proof is given by M. A. Akçoğlu [1]. R. Emilion and B. Hachem [7] also proved the same theorem, but with an extra assumption on the process (see also [1]). The proof of this theorem for superadditive processes with respect to a Markovian semigroup of operators on L 1 is given by M. A. Akçoğlu and U. Krengel [4]. Thus [1] and [9] extend the result of [4] to the sub-Markovian setting. Here we will obtain the multiparameter sub-Markovian version of this theorem, namely Theorem 3.17 below

Détail

DOI : 10.4153/CJM-1985-023-6

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