Stochastic Differential Mean-Field Games in a Weak Formulation

We study a Mean Field Game system in a weak formulation through its associated McKean-Vlasov Forward-Backward Stochastic Differential Equation (FBSDE). Our main goal is to obtain existence and regularity results of this FBSDE using the techniques of Malliavin calculus, in particular, classical and Malliavin differentiability. Using these results, we characterize the decoupling (master) field.Comment: 21 page

Things Behind Bayes’ Theorem A review of Sharon Bertsch McGrayne’s The theory that would not die: How Bayes\u27 theorem allowed to decipher the enigma code, to pursue the Russian submarines and to emerge triumphant from two centuries of controversy from a statistics education perspective

A feeling emerges from reading McGrayne’s book expressed as a paraphrase of a verse from Hamlet: There are more things behind Bayes’ theorem, Horatio, than dreamt of in your philosophy. The book tells a story of the birth and survival of an idea around which social enterprises, personal odysseys, and human passions are masterfully woven by the author. The book has 17 chapters distributed in five parts and two annexes. These parts reveal a narrative structure worthy of Propp: The hero of the story (Bayes’ theorem) is born and raised normally but rejected later. It is forced to act in secret but returns to the light and is submitted to several tests. The hero emerges triumphant from all of them. The above is just an outline of a complex but accessible chronicle that includes many brilliant and fascinating figures and extraordinary situations. We recommend the following three reviews that undoubtedly motivate you to immerse yourself in reading the book: Paulos (2011), Wainer & Savage (2012) and McGrayne (2015)