Results 111 to 120 of about 233 (151)
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Theory of Probability & Its Applications, 1989
See the review in Zbl 0646.60054.
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See the review in Zbl 0646.60054.
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On Amarts with Continuous Time
Theory of Probability & Its Applications, 1995The author introduces a class of continuous time processes called \(D_v\)-amarts which generalize the notion of martingales. Conditions when those processes have left-continuous (right-continuous) modifications of the trajectories are obtained. This paper is the continuation of the author's previous paper about discrete time \(D_v\)-amarts [ibid.
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On $(B,\rho )$-Amarts and Almost Sure Convergence
Theory of Probability & Its Applications, 1996The main aim of this paper is to generalize a conditional amart [\textit{D. Szynal} and the second author, Bull. Pol. Acad. Sci., Math. 34, 635-642 (1986; Zbl 0615.60027), the second author, Theory Probab. Appl. 36, No. 3, 637-639 (1991) and Teor. Veroyatn. Primen. 36, No. 3, 616-617 (1991; Zbl 0739.60036)] and a \(D_v\)-amart [\textit{I.
Kruk, L., Ziȩba, W.
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Optional Sampling Theorem and Representation of Set-Valued Amart
, 2007 Shoumei Li, Li Guan
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Convergence theorems for set-valued amarts and uniform amarts
Analysis Mathematica, 1996We continue our study of set-valued random processes initiated e.g. in [Proc. Indian Acad. Sci., Math. Sci. 101, No. 2, 63-70 (1991; Zbl 0756.28007)]. In this and other works, we concentrated our attention primarily to set-valued martingales and semi-martingales (i.e., set-valued submartingales and supermartingales).
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Convergence of Classes of Amarts Indexed by Directed Sets
Canadian Journal of Mathematics, 1980Let be a probability space, J a directed set filtering to the right. (X t) t∈J is a family of random variables adapted to an increasing family of σ-algebras . Vitali conditions V and V' on the σ-algebras, abstracting classical assumptions in Lebesgue's derivation theory, were made to insure essential convergence of martingales and submartingales ...
Millet, Annie, Sucheston, Louis
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On Some Properties of Conditional Amarts
Theory of Probability & Its Applications, 1992It is well known that if the supremum of an adapted sequence is integrable, then the sequence is an amart iff it is almost surely convergent. The author studies relationships between conditional amarts, \(D_ v\)-amarts and almost sure convergence. Typically, every \(D_ v\)- amart converges almost surely and every adapted, almost surely convergent ...
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On vector-valued amarts and dimension of banach spaces
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1977If (Xn)n~ N is an amart of class (B) taking values in a Banach space with the Radon-Nikodym property, then Xn converges weakly a.s., as proved in [4]. Examples exist in [4] and [7] which show that strong convergence may fail, but recently Alexandra Bellow [2] proved the following result: A Banach space E is finite-dimensional if (and only if) every E ...
Edgar, G. A., Sucheston, L.
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