MARTINGALE SELECTION THEOREM FOR A STOCHASTIC SEQUENCE WITH RELATIVELY OPEN CONVEX VALUES (2006)
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BibTeX
@MISC{Rokhlin06martingaleselection,
author = {Dmitry B. Rokhlin},
title = {MARTINGALE SELECTION THEOREM FOR A STOCHASTIC SEQUENCE WITH RELATIVELY OPEN CONVEX VALUES},
year = {2006}
}
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Abstract
Abstract. For a set-valued stochastic sequence (Gn) N n=0 with relatively open convex values Gn(ω) we give a criterion for the existence of an adapted sequence (xn) N n=0 of selectors, admitting an equivalent martingale measure. Mentioned criterion is expressed in terms of supports of the regular conditional upper distributions of the elements Gn. This result is a refinement of the main result of author’s previous paper (Teor. Veroyatnost. i Primen., 2005, 50:3, 480–500), where the sets Gn(ω) were assumed to be open and where were asked if the openness condition can be relaxed.
