On representation and regularity of continuous parameter multivalued martingales
نویسندگان
چکیده
منابع مشابه
On Representation and Regularity of Continuous Parameter Multivalued Martingales
In this paper we study multivalued martingales in continuous time. First we show that every multivalued martingale in continuous time can be represented as the closure of a sequence of martingale selections. Then we prove two results concerning the cadlag modifications of continuous time multivalued martingales, in Kuratowski-Mosco convergence and in convergence in the Hausdorff metric respecti...
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The existence of martingale selectors for a multivalued supermartin-gale with continuous parameter is proved.We also prove the weak regularity of multivalued supermartingales.Using the regularity of Banach-valued martingales,we show a multivalued supermartingale has a cadlag modiication under Kuratowski convergence. x1. Introduction Multivalued martingales and supermartingales with discrete par...
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Throughout these notes, (Ω,F ,P ) will be a probability space and F := {Ft }t∈J a filtration indexed by J , where J is an interval, usually J = [0,∞). The filtration F is said to be complete if each Ft contains all sets of measure 0, and is right-continuous if Ft =∩s>t Fs . A standard filtration is a filtration that is both complete and right-continuous. A stochastic process {X t }t≥0 defined o...
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We prove a variant of the abstract probabilistic version of Szemerédi’s regularity lemma, due to Tao, which applies to a number of structures (including graphs, hypergraphs, hypercubes, graphons, and many more) and works for random variables in Lp for any p > 1. Our approach is based on martingale difference sequences.
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Let (fn) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (dn) from [0, 1] such that ∫ 1 0 dn(x1, . . . , xn)dxn = 0 for almost all x1, . . . , xn−1, and such that the law of (fn) is the same as the law of ( ∑n k=1 dk(x1, . . . , xk)). Similar results for tangent sequences and sequences satisfying condition (C.I.) are presented. We also present a weaker...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04726-1