A note on Lorentz-invariant Markov processes

Abstract

This note will remove some unnecessary regularity assumptions from my first paper on the subject [1]. There, beyond the conditions of spatial and temporal homogeneity, Lorentz-invariance, the Markov property, and the requirement that speeds be less than that of light, there were additional assumptions: continuity in probability ((E), p. 248) and existence of derivatives with probability one at each time (first half of (C), p. 248). Both these assumptions will be shown to follow from the others. This makes easier the proof of the converse part of the main theorem of [1], Theorem 8.2, as will be indicated below.