Markov or non-Markov property of cM-X processes
نویسندگان
چکیده
منابع مشابه
Markov Property of Monotone Lévy Processes
Monotone Lévy processes with additive increments are defined and studied. It is shown that these processes have natural Markov structure and their Markov transition semigroups are characterized using the monotone Lévy-Khintchine formula. 17 Monotone Lévy processes turn out to be related to classical Lévy processes via Attal's " remarkable transformation. " A monotone analogue of the family of e...
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© Springer-Verlag, Berlin Heidelberg New York, 1976, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) 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 impressio...
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We consider a type of Markov property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A set-indexed generator is defined such that it completely characterizes the distribution of the process.
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The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.
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It is emphasized that non-Markovian processes, which occur for instance in the case of colored noise, cannot be considered merely as corrections to the class of Markov processes but require special treatment. Many familiar concepts, such as rst-passage times, no longer apply and need be reconsidered. Several methods of dealing with non-Markov processes are discussed. As an example a recent appl...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2004
ISSN: 0025-5645
DOI: 10.2969/jmsj/1191418643