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71.
In this article, some necessary and sufficient conditions are shown in order that the inequality of the form Ф1(λ)Pu(f^*〉λ)≤Ev (Ф2(C|f∞|)) holds with some constant C 〉 0 independent of martingale f = (fn)n≥0 and λ 〉 0, where Фl and Ф2 are a pair of Young functions, f^*=sup n≥0|fn| adn f∞=lim n→∞ fn a.e. 相似文献
72.
Stefan Ankirchner Peter Imkeller Alexandre Popier 《Stochastic Processes and their Applications》2009,119(9):2744-2772
We consider backward stochastic differential equations (BSDEs) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the generator is seen as vanishing, so that the classical solution can be reconstructed by a combination of the operations of conditioning and using martingale representations. For the case where the terminal condition is bounded and the generator fulfills the usual continuity and boundedness conditions, we show that measure solutions with equivalent measures just reinterpret classical ones. For the case of terminal conditions that have only exponentially bounded moments, we discuss a series of examples which show that in the case of non-uniqueness, classical solutions that fail to be measure solutions can coexist with different measure solutions. 相似文献
73.
We present a general framework for solving stochastic porous medium equations and stochastic Navier–Stokes equations in the sense of martingale solutions. Following Krylov [N.V. Krylov, The selection of a Markov process from a Markov system of processes, and the construction of quasidiffusion processes, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 691–708] and Flandoli–Romito [F. Flandoli, N. Romito, Markov selections for the 3D stochastic Navier–Stokes equations, Probab. Theory Related Fields 140 (2008) 407–458], we also study the existence of Markov selections for stochastic evolution equations in the absence of uniqueness. 相似文献
74.
75.
刘培德 《数学物理学报(A辑)》2010,30(5):1292-1305
弱型空间是近年来调和分析与鞅论中倍受关注的研究方向, 该文就以下几方面介绍有关弱型鞅空间的研究工作:(1) Lorentz鞅空间的原子分解;(2) Orlicz鞅空间的强弱型加权不等式; (3) 弱Orlicz鞅空间与拟范数不等式; (4) 在Banach空间理论与二进域调和分析中的应用. 相似文献
76.
William Leeb 《Applied and Computational Harmonic Analysis》2018,44(3):584-610
This paper develops a theory of harmonic analysis on spaces with tree metrics, extending previous work in this direction by Gavish, Nadler and Coifman (2010) [30] and Gavish and Coifman (2011, 2012) [28], [29]. We show how a natural system of martingales and martingale differences induced by a partition tree leads to simple and effective characterizations of the Lipschitz norm and its dual for functions on a single tree metric space. The restrictions we place on the tree metrics are far more general than those considered in previous work. As the dual norm is equal to the Earth Mover's Distance (EMD) between two probability distributions, we recover a simple formula for EMD with respect to tree distances presented by Charikar (2002) [36].We also consider the situation where an arbitrary metric is approximated by the average of a family of dominating tree metrics. We show that the Lipschitz norm and its dual for the tree metrics can be combined to yield an approximation to the corresponding norms for the underlying metric.The main contributions of this paper, however, are the generalizations of the aforementioned results to the setting of the product of two or more tree metric spaces. For functions on a product space, the notion of regularity we consider is not the Lipschitz condition, but rather the mixed Lipschitz condition that controls the size of a function's mixed difference quotient. This condition is extremely natural for datasets that can be described as a product of metric spaces, such as word-document databases. We develop effective formulas for norms equivalent to the mixed Lipschitz norm and its dual, and extend our results on combining pairs of trees. 相似文献
77.
We prove a central limit theorem for strictly stationary random fields under a sharp projective condition. The assumption was introduced in the setting of random sequences by Maxwell and Woodroofe. Our approach is based on new results for triangular arrays of martingale differences, which have interest in themselves. We provide as applications new results for linear random fields and nonlinear random fields of Volterra-type. 相似文献
78.
In this paper, we first study the martingale problem in a sublinear expectation space. The critical tool is the Evans–Krylov theorem on regularity properties for solutions of fully nonlinear PDEs. Based on the analysis for the martingale problem and inspired by the rough path theory, we then develop stochastic calculus with respect to a general stochastic process, and derive an Itô type formula and the integration-by-parts formula. Our framework is analytic in that it does not rely on the probabilistic concept of “independence” as in the -expectation theory. 相似文献
79.
Claudio Fontana 《Stochastic Processes and their Applications》2018,128(3):1007-1033
We study the strong predictable representation property in filtrations initially enlarged with a random variable . We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the existing martingale representation results and does not rely on the equivalence between the conditional and the unconditional laws of . Depending on the behavior of the density process at zero, different forms of martingale representation are established. The results are illustrated in the context of hedging contingent claims under insider information. 相似文献
80.
Rémi Peyre 《Potential Analysis》2008,29(1):17-36
Carne’s bound is a sharp inequality controlling the transition probabilities for a discrete reversible Markov chain (Section 1).
Its ordinary proof uses spectral techniques which look as efficient as miraculous. Here we present a new proof, comparing
a “drift” for ways “out” and “back”, to get the gaussian part of the bound (Section 2), and using a conditioning technique
to get the flight factor (Section 4). Moreover we show how our proof is more “supple” than Carne’s one and may generalize
(Section 3.2).
相似文献