Clark formula and logarithmic Sobolev inequalities for Bernoulli measures

Using a Clark formula for the predictable representation of random variables in discrete time and adapting the method presented in Electron. Commun. Probab. 2 (1997) 71–81] in the Brownian case, we obtain a proof of modified and L¹ logarithmic Sobolev inequalities for Bernoulli measures. We also prove a bound that improves these inequalities as well as the optimal constant inequality of J. Funct. Anal. 156 (2) (1998) 347–365]. To cite this article: F. Gao, N. Privault, C. R. Acad. Sci. Paris, Ser. I 336 (2003).