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Characterisation of L0-boundedness for a general set of processes with no strictly positive element

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  • Bálint, Dániel Ágoston

Abstract

We consider a general set X of adapted nonnegative stochastic processes in infinite continuous time. X is assumed to satisfy mild convexity conditions, but in contrast to earlier papers need not contain a strictly positive process. We introduce two boundedness conditions on X — DSV corresponds to an asymptotic L0-boundedness at the first time all processes in X vanish, whereas NUPBRloc states that Xt={Xt:X∈X} is bounded in L0 for each t∈[0,∞). We show that both conditions are equivalent to the existence of a strictly positive adapted process Y such that XY is a supermartingale for all X∈X, with an additional asymptotic strict positivity property for Y in the case of DSV.

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  • Bálint, Dániel Ágoston, 2022. "Characterisation of L0-boundedness for a general set of processes with no strictly positive element," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 51-75.
    • Handle: RePEc:eee:spapps:v:147:y:2022:i:c:p:51-75
    DOI: 10.1016/j.spa.2021.12.013
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    References listed on IDEAS

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