On the Integration of Diffusion Equations in Riemannian Spaces
Kôsaku Yosida · Proceedings of the American Mathematical Society · 1952
KÔSAKU YOSIDA1. Introduction.Let R he a connected domain of an infinitely differentiable, orientable, w-dimensional (m ^ 2) Riemannian space with the metric ds2 = gij(x)dxidx1'.Under a certain "continuity condition" of Lindeberg's type, the temporally homogeneous stochastic process in R is governed by a pair of equations:1 ,. ., df(x, t) d2f(x, t) df(x, t)-^((g(x)y'2a2 dx*