The Radial Part of a $\Gamma$-Martingale and a Non-Implosion Theorem

Abstract

An upper bound is given for the behaviour of the radial part of a $\Gamma$-martingale, generalizing previous work of the author on the radial part of Riemannian Brownian motion. This upper bound is applied to establish an integral curvature condition to determine when $\Gamma$-martingales cannot "implode" in finite intrinsic time, answering a question of Emery and generalizing work of Hsu on the $C_0$-diffusion property of Brownian motion.