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Fu Qing Gao 《数学学报(英文版)》2009,25(2):209-222
Three types of laws of the iterated logarithm (LIL) for locally square integrable martingales with continuous parameter are considered by a discretization approach. By this approach, a lower bound of LIL and a number of FLIL are obtained, and Chung LIL is extended. 相似文献
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R. Bórquez 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(2):165-171
The property of countable convexity of the set which contains all dominated martingale laws, for a family of measurable functions with values in a separable Borel space, is proved to be equivalent to the existence of a sufficient statistic. The result is then used to derive a representation of such laws in terms of their extreme points, which are laws of uniformly integrable martingales. Finally, we show that martingales with sufficient statistics converge with probability 1. 相似文献
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Ferenc Weisz 《Journal of Theoretical Probability》1996,9(2):301-316
With the help of two-parameter martingales and strong martingales Hardy spaces consisting of adapted function sequences are considered. The Hardy spaces generated by the square and by the conditional square functions and their dual spaces are investigated. An inequality due to Stein and Lepingle is extended to two parameters.This research was supported by the Hungarian Scientific Research Funds No. 2085 and No. 74189 as well as by DAAD, the lattest with a stay at the Ludwig-Maximilians-Universität in München. 相似文献
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B值渐近鞅是B值鞅的重要推广,它保持了鞅的一些是一性质,然后对B值渐近鞅的局部收敛性很少有文献论及。本文利用B值渐近鞅的Doob分解,对B值渐近鞅的局部收敛性作些探讨,得到了B值渐近鞅局部收敛性的几个结果,它们是鞅的有关结论的推广与改进。 相似文献
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Consider a continuous local martingale X. We say that X satisfies the representation property if any martingale Y of X can be represented as stochastic ITÔ integral of X. On the basis of part I of the present paper, in section 4 several general examples of continuous local martingales X satisfying the representation property are given: Stochastic continuous GAUSSian martingales, processes with conditionally independent increments, stopped continuous local martingales, random time change of WIENER processes, weak solutions of stochastic differential equations. Theorem 7 states that every (homogeneous) continuous strong MARKOV local martingale has the representation property. In section 5, the results of part I are applied to n-dimensional continuous local martingales and analogous representation results are obtained. In section 6, we consider an application of section 5 to the n-dimensional time change for reducing every n-dimensional continuous local martingale with orthogonal components to the WIENER process. This improves a theorem of F. B. KNIGHT and simplifies its proof considerably. 相似文献
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R. M. Huggins 《Probability Theory and Related Fields》1985,69(2):243-250
Summary A Skorokhod embedding approach is used to give functional laws of the iterated logarithm which involve the process up to timen in the reverse martingale case and the tail of the process in the martingale case. This complements the more usual versions
of the iterated logarithm laws for martingales and reverse martingales. 相似文献
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We characterize a Brownian motion indexed by a semilattice of sets, using the theory of set-indexed martingales: a square integrable continuous set-indexed strong martingale is a Brownian motion if and only if its compensator is deterministic and continuous.Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada.Research done while this author was visiting the University of Ottawa. He wishes to thank Professor Ivanoff for her kind hospitality. 相似文献
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《Stochastic Processes and their Applications》2001,93(1):109-117
Bernstein-type inequalities for local martingales are derived. The results extend a number of well-known exponential inequalities and yield an asymptotic inequality for a sequence of asymptotically continuous martingales. 相似文献
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In this paper, we present a unified framework for our previous constructions of martingales with the same one-dimensional marginals as particular cases of processes increasing in the convex order. This framework encompasses our former uses of Lévy sheets, Sato sheets and self-decomposable laws. New examples of processes increasing in the convex order are also exhibited, but we do not know how to associate to them martingales with the same one-dimensional marginals. 相似文献
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Analogs of the Kolmogorov, Zygmund-Martsenkevich, and Brunk-Prokhorov strong law of large numbers are proved for martingales
with continuous parameter. A new generalization of the Brunk—Prokhorov strong law of large numbers is given for martingales
with discrete times. Along with convergence almost everywhere, we also prove the average convergence. 相似文献
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Fabio Gagliardi Cozman 《International Journal of Approximate Reasoning》2010,51(9):1069-1084
his paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda’s recent inequalities and laws of large numbers. The proofs indicate connections between the theory of martingales and concepts of epistemic and regular irrelevance. 相似文献
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Akimichi Takemura Vladimir Vovk Glenn Shafer 《Annals of the Institute of Statistical Mathematics》2011,63(5):873-885
We prove game-theoretic generalizations of some well-known zero-one laws. Our proofs make the martingales behind the laws
explicit, and our results illustrate how martingale arguments can have implications going beyond measure-theoretic probability. 相似文献
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We prove a theorem on the strong law of large numbers for martingales. The existence of higher moments is not assumed. From the theorem proved, we deduce numerous well-known results on the strong law of large numbers both for martingales and for sequences of sums of independent random variables. 相似文献
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We prove the strong law of large numbers for vector martingales with arbitrary operator normalizations. From the theorem proved, we deduce several known results on the strong law of large numbers for martingales with continuous time. 相似文献
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P. A. Mykland 《Probability Theory and Related Fields》1995,103(4):475-492
The paper develops a way of embedding general martingales in continuous ones in such a way that the quadratic variation of the continuous martingale has conditional cumulants (given the original martingale) that are explicitly given in terms of optional and predictable variations of the original process. Bartlett identities for the conditional cumulants are also found. A main corollary to these results is the establishment of second (and in some cases higher) order asymptotic expansions for martingales.Research supported in part by National Science Foundation grant DMS 93-05601 and Army Research Office grant DAAH04-1-0105 相似文献
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本文给出B值拟鞅的概率不等式与集合不等式,并用它们刻划了B空间的p可光滑性及q可凸性,作为应用,还证明了B值拟鞅的强大数律,收敛速度及极大值函数的可积性。 相似文献
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