## Les processus de Dirichlet en tant qu’espace de Banach. (Dirichlet processes as Banach spaces).(French)Zbl 0602.60069

What is called a Dirichlet process is any sum of a square integrable martingale and a process of vanishing quadratic variation (plus some natural assumptions of adaptivity and continuity), but when the last is defined the partitions of the time interval [0,1] are supposed to be defined by stopping times rather than fixed times. The class $${\mathcal D}$$ of all such processes is proved to be a Banach space in which semimartingales are dense. When the process $$X_ t$$, $$t\in [0,1]$$, and the function F obey certain conditions it is proved that $$F(X_ t)- F(X_ 0)$$ is a Dirichlet process and its martingale part is explicitly given. A necessary condition and a sufficient condition is found for a function f so that $$f(B_ t)$$ is a Dirichlet process $$(B_ t$$ is the Brownian motion).
Reviewer: O.Enchev

### MSC:

 60J60 Diffusion processes 60J65 Brownian motion 60G44 Martingales with continuous parameter
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### References:

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