Supermartingale Deomposition with General Index Set
Gianluca Casseses
TL;DR
This paper establishes conditions for the existence of Doob-Meyer decompositions and Doleans-Dade measures for supermartingales indexed by arbitrary index sets, extending classical stochastic process theory.
Contribution
It generalizes the Doob-Meyer decomposition and Doleans-Dade measure existence results to supermartingales with general index sets, broadening their applicability.
Findings
Proves existence of Doleans-Dade measures for general index set supermartingales.
Establishes Doob-Meyer decomposition under new conditions.
Extends classical results to more general stochastic process frameworks.
Abstract
We prove results on the existence of Dol\'{e}ans-Dade measures and of the Doob-Meyer decomposition for supermartingales indexed by a general index set
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Stochastic processes and financial applications · Advanced Banach Space Theory