grandes-ecoles 2024 Q13

grandes-ecoles · France · mines-ponts-maths1__pc Continuous Probability Distributions and Random Variables Entropy, Information, or Log-Sobolev Functional Analysis

For $t \in \mathbf{R}_+$, we set $S(t) = \operatorname{Ent}_{\varphi}(P_t(f))$. Justify that $S(t)$ is well defined.

For $t \in \mathbf{R}_+$, we set $S(t) = \operatorname{Ent}_{\varphi}(P_t(f))$. Justify that $S(t)$ is well defined.