Talk:Stochastic processes and boundary value problems

Rename to Kakutani solution

I propose renaming Stochastic processes and boundary value problems to Kakutani's solution to the classical Dirichlet problem or perhaps the shorter Kakutani solution. The reson for this is that the general topic of "stochastic processes and boundary value problems" is already covered more extensively and in greater depth in two existing articles: the Fokker–Planck equation and the Feynman–Kac formula. These are in turn surrounded by a passel of interconnected articles, including Kolmogorov equations, Kolmogorov backward equations (diffusion) and Klein–Kramers equation, which in turn point at ways of deriving needed results, everything from the Kramers–Moyal expansion to the Infinitesimal generator (stochastic processes). Most of these articles repeat the eqn for the Itô process, and so we see this presented over and over, with variations of notation. Most of these articles then convert it to a second-order differential equation, again, with (mostly minor) differences in notation.

To somehow repeat all of that in a generic "stochastic processes and boundary value problems" seems silly. However, the current article does present the Kakutani solution in a rather direct and fairly elegant fashion, using notation that is a bit cleaner and more sophisticated than the rest. So, rather than expanding this article to encompass more, I suggest renaming it for the topic that it already covers quite well. (Reposting this to WP:M for discussion.) 67.198.37.16 (talk) 17:37, 7 May 2025 (UTC)