Finitely additive supermartingales are differences of martingales and adapted increasing processes

Armstrong, Thomas E.

doi:10.1090/S0002-9939-1985-0810174-8

Finitely additive supermartingales are differences of martingales and adapted increasing processes
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Proc. Amer. Math. Soc. 95 (1985), 619-625 Request permission

Abstract:

It is shown that any nonnegative bounded supermartingale admits a Doob-Meyer decomposition as a difference of a martingale and an adapted increasing process upon appropriate choice of a reference probability measure which may be only finitely additive.

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