共查询到20条相似文献,搜索用时 31 毫秒
1.
N. A. Kolodii 《Journal of Mathematical Sciences》2006,137(1):4531-4540
We investigate the properties of random fields related to stochastic intergals with respect to a two-parameter strong square-integrable
martingale in the case where the martingale and the integrands depend on the limits of integration. We prove inequalities
for the moments of the uniform norm and the modulus of continuity of trajectories of modifications of such fields. Bibliography:
8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 80–96. 相似文献
2.
Duality theorem for B‐valued martingale Orlicz–Hardy spaces associated with concave functions
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Lin Yu 《Mathematische Nachrichten》2016,289(5-6):756-774
The dual space of B ‐valued martingale Orlicz–Hardy space with a concave function Φ, which is associated with the conditional p‐variation of B ‐valued martingale, is characterized. To obtain the results, a new type of Campanato spaces for B ‐valued martingales is introduced and the classical technique of atomic decompositions is improved. Some results obtained here are connected closely with the p‐uniform smoothness and q‐uniform convexity of the underlying Banach space. 相似文献
3.
Nakahiro Yoshida 《Probability Theory and Related Fields》1997,109(3):301-342
Summary. We present an asymptotic expansion of the distribution of a random variable which admits a stochastic expansion around a
continuous martingale. The emphasis is put on the use of the Malliavin calculus; the uniform nondegeneracy of the Malliavin
covariance under certain truncation plays an essential role as the Cramér condition did in the case of independent observations.
Applications to statistics are presented.
Received: 5 September 1995 / In revised form: 20 October 1996 相似文献
4.
Coenraad C.A. Labuschagne Valeria Marraffa 《Journal of Mathematical Analysis and Applications》2010,363(2):357-365
We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon-Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney-Schaefer l-tensor product , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon-Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on . Secondly, we derive a Riesz decomposition for uniform amarts of maps acting between a Banach lattice and a Banach space. This result is used to characterize Banach spaces with the Radon-Nikodým property in terms of uniformly norm bounded uniform amarts of maps that are norm convergent. In the case 1<p<∞, our results yield Lp(μ,Y)-space analogues of some of the well-known results on uniform amarts in L1(μ,Y)-spaces. 相似文献
5.
François Coquet Ying Hu Jean Mémin Shige Peng 《Probability Theory and Related Fields》2002,123(1):1-27
From a general definition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive,
under rather general assumptions, the notions of conditional nonlinear expectation and nonlinear martingale. We prove that
any such nonlinear martingale can be represented as the solution of a backward stochastic equation, and in particular admits
continuous paths. In other words, it is a g-martingale.
Received: 2 February 2000 / Revised version: 1 June 2001 / Published online: 13 May 2002 相似文献
6.
Banach空间值鞅变换的有界性及其应用 总被引:7,自引:0,他引:7
本文给出关于Banach空间值鞅变换算子有界性的一种新的处理方法,得到一系列带有广泛性的结果,并应用鞅变换算子的有界性刻画了Banach空间的一致光滑性和一致凸性,使得许多已有文献中的结论成为本文的特例. 相似文献
7.
Shlomo Levental 《Journal of Theoretical Probability》1989,2(3):271-287
This paper develops a method to get empirical central limit theorems for martingale differences that are uniformly bounded. The main idea is to generalize to martingales some ideas of E. Gine and J. Zinn [Ann. Prob.
12, 929–989 (1984)]. We consider two examples: An extension of a theorem of R. Dudley from i.i.d. to a certain type of Markov chain, and a uniform CLT for the baker's transformation. 相似文献
8.
Wlodzimierz Bryc Wojciech Matysiak Jacek Wesolowski 《Transactions of the American Mathematical Society》2007,359(11):5449-5483
We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a -commutation relation. This implies that quadratic harnesses are essentially determined uniquely by five numerical constants. Explicit recurrences for the orthogonal martingale polynomials are derived in several cases of interest.
9.
We study the Abelian sandpile model on . In d ≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit μ of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure μ, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves
and uniform two-component spanning trees and results on the uniform spanning forest measure on .
相似文献
10.
The convergence of stochastic processes indexed by parameters which are elements of a metric space is investigated in the context of an invariance principle of the uniform central limit theorem (UCLT) for stationary Markov chains. We assume the integrability condition on metric entropy with bracketing. An eventual uniform equicontinuity result is developed which essentially gives the invariance principle of the UCLT. We translate the problem into that of a martingale difference sequence as in Gordin and Lifsic.(7) Then we use the chaining argument with stratification adapted from that of Ossiander.(11) The results of this paper generalize those of Levental(10) and Ossiander.(11) 相似文献
11.
He Shuyuan 《数学年刊B辑(英文版)》1995,16(3):331-340
UNIFORMCONVERGENCYFORWEIGHTEDPERIODOGRAMOFSTATIONARYLINEARRANDOMFIELDS¥HESHUYUANAbstract:Let{Xn;n∈N2}beatwodimensionallyindex... 相似文献
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14.
Kwok-Pun HO 《数学物理学报(B辑英文版)》2018,38(1):93-109
We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces. 相似文献
15.
We compute and then discuss the Esscher martingale transform for exponential processes, the Esscher martingale transform for linear processes, the minimal martingale measure, the class of structure preserving martingale measures, and the minimum entropy martingale measure for stochastic volatility models of the Ornstein–Uhlenbeck type as introduced by Barndorff-Nielsen and Shephard. We show that in the model with leverage, with jumps both in the volatility and in the returns, all those measures are different, whereas in the model without leverage, with jumps in the volatility only and a continuous return process, several measures coincide, some simplifications can be made and the results are more explicit. We illustrate our results with parametric examples used in the literature. 相似文献
16.
C. Rainer 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):65-98
The aim of this paper is to study backward stochastic differential equations (BSDE) driven by Azéma's martingale and the associated deterministic functional equations. More precisely, we introduce BSDE's vs. Azéma's martingale in a general frame, then we prove that the existence of a solution to a Markovian BSDE implies the existence of a solution to a deterministic functional equation of a new type. Uniqueness for the functional equation is proved in a particular case. Then we discuss BSDE's vs. an asymmetric martingale: half Brownian motion/half Azéma's martingale, which leads to an asymmetric deterministic functional equation. 相似文献
17.
W. R. Wade 《Proceedings of the American Mathematical Society》2003,131(9):2877-2881
There are a number of papers in the literature which contain Cesàro analogues of results already known for martingale sums of Vilenkin-Fourier series. We show that for Vilenkin systems of bounded type, these are not merely analogues but actually generalizations. Indeed, we prove that convergence of the Cesàro means of a Vilenkin series implies convergence of martingale partial sums of itself.
18.
Marcus Brazil Benny K. Nielsen Pawel Winter Martin Zachariasen 《Computational Geometry》2004,29(3):251-263
We consider the problem of finding a minimum spanning and Steiner tree for a set of n points in the plane where the orientations of edge segments are restricted to λ uniformly distributed orientations, λ=2,3,4,… , and where the coordinate system can be rotated around the origin by an arbitrary angle. The most important cases with applications in VLSI design arise when λ=2 or λ=4. In the former, so-called rectilinear case, the edge segments have to be parallel to one of the coordinate axes, and in the latter, so-called octilinear case, the edge segments have to be parallel to one of the coordinate axes or to one of the lines making 45° with the coordinate axes (so-called diagonals). As the coordinate system is rotated—while the points remain stationary—the length and indeed the topology of the minimum spanning or Steiner tree changes. We suggest a straightforward polynomial-time algorithm to solve the rotational minimum spanning tree problem. We also give a simple algorithm to solve the rectilinear Steiner tree problem in the rotational setting, and a finite time algorithm for the general Steiner tree problem with λ uniform orientations. Finally, we provide some computational results indicating the average savings for different values of n and λ both for spanning and Steiner trees. 相似文献
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20.
《Topology and its Applications》1987,27(2):113-127
Let T be the forgetful functor from uniform spaces to completely regular topological spaces. We study T-sections, i.e. functors right inverse to T. We develop as tool the notion of spanning a T-section by a class of uniform spaces, and the order-dual notion of cospanning. Coarsest and finest uniform bireflectors and coreflectors associated with a T-section are characterized. Certain effects of the uniform completion reflector on a T-section are expressed in terms of the associated bireflectors. 相似文献