A New Proof of Robbins-Siegmund Almost Supermartingale Theorem
L.A. Portela, R.H.C. Takahashi, B.N.B. de Lima, R.S. dos Santos
2025, v.31, Issue 3-4, 233-238
ABSTRACT
We establish a theorem for stopped non-negative almost supermartingales, analogous to the stopped martingale theorem. Our result builds upon the definition of a stopped process and turns the proof of Proposition 1 in [4] into an application of this theorem. However, for its demonstration, we used fundamental concepts and theorems from probability theory, avoiding the use of local martingale properties as was done in [4]. Furthermore, we present an extended version of Doob’s maximal inequality reformulated for non-negative almost supermartingales
doi:10.61102/1024-2953-mprf.2025.31.3-4.003
Keywords: Non-negative almost supermartingales, stopped process
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