Calcul stochastique et problèmes de martingales / J. Jacod

Auteur: Jacod, Jean (1944-) - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 714Langue: françaisPays: AllemagneÉditeur: Berlin : Springer-Verlag, 1979Description: 1 vol. (X-539 p.) ; 25 cm ISBN: 3540092536 ; br. Résumé: This work is a fundamental monograph devoted to the rapidly growing branch of the theory of random processes in which the notions of martingale and semimartingale play central roles. The new theory is based on the general theory of random processes, and makes extensive use of methods from measure theory and integration, functional analysis and differential equations. Within the framework of the new theory it is possible to consider from a common point of view classical problems that were previously solved for various special classes of random processes: filtering, absolutely continuous change of measure, and behavior of processes at infinity. Finally, the generality of the approach makes it possible to obtain results for sequences, i.e., processes with discrete time, as a special case of theorems for the case of a continuous time parameter. ... (MathSciNet).Bibliographie: Bibliogr. p. [527]-539. Index. Sujets MSC: 60G44 Probability theory and stochastic processes -- Stochastic processes -- Martingales with continuous parameter
60G57 Probability theory and stochastic processes -- Stochastic processes -- Random measures
60H05 Probability theory and stochastic processes -- Stochastic analysis -- Stochastic integrals
60H20 Probability theory and stochastic processes -- Stochastic analysis -- Stochastic integral equations
93E11 Systems theory; control -- Stochastic systems and control -- Filtering
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Bibliogr. p. [527]-539. Index

This work is a fundamental monograph devoted to the rapidly growing branch of the theory of random processes in which the notions of martingale and semimartingale play central roles. The new theory is based on the general theory of random processes, and makes extensive use of methods from measure theory and integration, functional analysis and differential equations. Within the framework of the new theory it is possible to consider from a common point of view classical problems that were previously solved for various special classes of random processes: filtering, absolutely continuous change of measure, and behavior of processes at infinity. Finally, the generality of the approach makes it possible to obtain results for sequences, i.e., processes with discrete time, as a special case of theorems for the case of a continuous time parameter. ... (MathSciNet)

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