A short nonstandard proof of the Doob-Meyer and Dol{\'e}ans-Dade theorems
Takashi Matsunaga
TL;DR
This paper presents a concise and elementary proof of the Doob-Meyer and D{é}l{é}ans-Dade theorems utilizing nonstandard analysis techniques.
Contribution
It introduces a novel nonstandard analysis approach to simplify and shorten the proofs of these fundamental stochastic process theorems.
Findings
Proofs are significantly shorter and more elementary.
Method demonstrates the power of nonstandard analysis in stochastic calculus.
Potential for broader application in probability theory.
Abstract
Using nonstandard analysis, a very short and elementary proof of the Doob-Meyer decomposition and the Dol{\'e}ans Dade theorems is provided.
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