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XIII: 54, 620-623, LNM 721 (1979)

**MEYER, Paul-André**

Caractérisation des semimartingales, d'après Dellacherie (Stochastic calculus)

This short paper contains the proof of a very important theorem, due to Dellacherie (with the crucial help of Mokobodzki for the functional analytic part). Namely, semimartingales are exactly the processes which give rise to a nice vector measure on the previsible $\sigma$-field, with values in the (non locally convex) space $L^0$. It is only fair to say that this direction was initiated by Métivier and Pellaumail, and that the main result was independently discovered by Bichteler,*Ann. Prob.* **9**, 1981)

Comment: An important lemma which simplifies the proof and has other applications is given by Yan in 1425

Keywords: Semimartingales, Stochastic integrals

Nature: Exposition

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Caractérisation des semimartingales, d'après Dellacherie (Stochastic calculus)

This short paper contains the proof of a very important theorem, due to Dellacherie (with the crucial help of Mokobodzki for the functional analytic part). Namely, semimartingales are exactly the processes which give rise to a nice vector measure on the previsible $\sigma$-field, with values in the (non locally convex) space $L^0$. It is only fair to say that this direction was initiated by Métivier and Pellaumail, and that the main result was independently discovered by Bichteler,

Comment: An important lemma which simplifies the proof and has other applications is given by Yan in 1425

Keywords: Semimartingales, Stochastic integrals

Nature: Exposition

Retrieve article from Numdam