Talk:Kolmogorov's inequality

This proof of Kolmogorov's maximal inequality is not the usual one, so there is an aspect of "original research" to this piece. I am also worried that the proof is not right (or not complete). One has to show that the expected squared increment of the Z's is smaller than that of the S's. This is not 100% clear. Why not give the conventional proof and conventional references and leave the new proof for another place.(Hatcheck (talk) 22:10, 23 April 2013 (UTC))[reply]

Martingale proofs of Kolmogorov's inequality are not uncommon, e.g.^[1] However, the proof as it stands is simply wrong. We may not assume without loss of generality that $S_{n}\geq 0$ .--Livingthingdan (talk) 10:24, 22 January 2014 (UTC)[reply]

^ Williams, David (1997). Probability with Martingales (Repr. ed.). Cambridge: Cambridge Univ. Press. p. 138. ISBN 0521406056.

[1] Williams, David (1997). Probability with Martingales (Repr. ed.). Cambridge: Cambridge Univ. Press. p. 138. ISBN 0521406056.

[1]