A variational proof of conditional expectation

Ponente(s): Hugo Guadalupe Reyna Castañeda, María de los Ángeles Sandoval Romero

In this talk, we prove that the conditional expectation of a random variable with finite second moment, given a σ-algebra, arises as the unique critical point of an energy functional defined in the Hilbert space L2. We then extend this characterization, by density, to all integrable random variables.