Results 151 to 160 of about 36,708 (189)

Weak atomic decomposition of B-valued martingales with two-parameters

Acta Mathematica Hungarica, 2010
\textit{R. Cheng} and \textit{G. Shixin} [Acta Math. Hung. 93, No.~1--2, 7--25 (2001; Zbl 1012.60048)] obtained atomic decompositions for B-valued martingales in the two-parameter case. In this paper, the authors define some weak atoms and prove atomic decomposition theorems in weak Hardy spaces.
Li, Y. F., Liu, P. D.
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The transformation theorem for two-parameter pure jump martingales

Probability Theory and Related Fields, 1991
Let M be a martingale of pure jump type, i.e. the compensation of the process describing the total of the point jumps of M in the plane. M can be uniformly approximated by martingales of bounded variation jumping only on finitely many axial parallel lines.
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Proof of existence theorems for the two-parameter martingale problem

Siberian Mathematical Journal, 1995
Following \textit{D. W. Stroock} and \textit{S. R. S. Varadhan} [Commun. Pure Appl. Math. 22, 345--400 (1969; Zbl 0167.43903)], the author considers existence theorems for two-parameter martingale problem. Briefly, the measure \(P\) is called a solution of martingale problem for \((z_0,x_0,a,b)\) if \(P\{x(z,\cdot)=x_0(z)\), \(z\in\partial I_{z_0}\}=1\)
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Planar seminartingales obtained by transformations of two-parameter martingales

1989
In this paper we study the weak local submartingale property and the quasimartingale property of processes obtained by the composition of a two-parameter continuous martingale by c2-functions whose second derivative is convex.
Nguyen Minh Duc, D. Nualart, M. Sanz
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On Parameter-Measurability of the Stochastic Integral with Respect to the Two-Parameter Strong Martingale

Theory of Probability & Its Applications, 2012
The aim of this article is to establish the existence of a good version of a parametrized family of two-parameters martingales given by stochastic integrals. More precisely, the main result roughly states that, given a measurable family \(\mu(0,x,\omega)\) of \(L^2\)-martingales (where \(0\) sums some measurable space, \(x\in (\mathbb{R}_+)^2 ...
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ON THE RATES OF CONVERGENCE IN THE CENTRAL LIMIT THEOREM FOR TWO-PARAMETER MARTINGALE DIFFERENCES

Acta Mathematica Scientia, 1996
Summary: We obtain the uniform bounds on the rate of convergence in the central limit theorem for a class of two-parameter martingale difference sequences under certain conditions.
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Inequalities and duality results with respect to two-parameter strong martingales

Analysis Mathematica, 1997
The author introduces the spaces \(\text{BMO}_q\) and \(\text{BMO}^-_q\) for two parameter strong martingales. The operator \(\sigma\) called the conditional quadratic variation with respect to \((\mathcal F^-_n =\mathcal F_{n_1,n_2-1} \lor \mathcal F_{n_1-1,n_2}\); \(n=(n_1,n_2)\in {\mathbb N}^2)\) is used. Besides the martingale Hardy spaces \(H^*_p\)
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The Davis inequalities and the Gundy decomposition for two-parameter strong martingales. I

1991
Let \(M=(M_ t)_{t\in\mathbb{R}^ 2_ +}\) be a right continuous, two- parameter strong martingale such that \(\mathbb{E}\sup_{s\leq t}M_ ...
Gushchin, A. A., Mishura, Yu. S.
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A generalized Itô formula for two-parameter martingales. II

1986
This article is a continuation of the previous work of the author on the same subject [ibid. 30, 114-127 (1984; Zbl 0563.60047); English translation in Theory Probab. Math. Stat. 30, 127-142 (1985)]. The present paper is devoted to establish a change of variable formula for two-parameter martingales which can be decomposed into four orthogonal ...
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Martingale transforms and fractional integrals on rearrangement-invariant martingale Hardy spaces

Periodica Mathematica Hungarica, 2020
Kwok-Pun Ho
exaly