Beurling–Deny formula of semi-Dirichlet forms

In this Note we announce a structure result for non-symmetric Dirichlet forms and semi-Dirichlet forms. Our result is regarded as an extension of the celebrated Beurling–Deny formula which is up to now available only for symmetric Dirichlet forms. The result can also be regarded as an extension of Lévy–Khinchine formula or more generally, an extension of Courrège's Theorem in the semi-Dirichlet forms setting. To cite this article: Z.-C. Hu, Z.-M. Ma, C. R. Acad. Sci. Paris, Ser. I 338 (2004).