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Search: All articles in the CMB digital archive with keyword martingale

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1. CMB 2016 (vol 59 pp. 528)

Jahan, Qaiser
Characterization of Low-pass Filters on Local Fields of Positive Characteristic
In this article, we give necessary and sufficient conditions on a function to be a low-pass filter on a local field $K$ of positive characteristic associated to the scaling function for multiresolution analysis of $L^2(K)$. We use probability and martingale methods to provide such a characterization.

Keywords:multiresolution analysis, local field, low-pass filter, scaling function, probability, conditional probability and martingales
Categories:42C40, 42C15, 43A70, 11S85

2. CMB 2011 (vol 55 pp. 597)

Osękowski, Adam
Sharp Inequalities for Differentially Subordinate Harmonic Functions and Martingales
We determine the best constants $C_{p,\infty}$ and $C_{1,p}$, $1 < p < \infty$, for which the following holds. If $u$, $v$ are orthogonal harmonic functions on a Euclidean domain such that $v$ is differentially subordinate to $u$, then $$ \|v\|_p \leq C_{p,\infty} \|u\|_\infty,\quad \|v\|_1 \leq C_{1,p} \|u\|_p. $$ In particular, the inequalities are still sharp for the conjugate harmonic functions on the unit disc of $\mathbb R^2$. Sharp probabilistic versions of these estimates are also studied. As an application, we establish a sharp version of the classical logarithmic inequality of Zygmund.

Keywords: harmonic function, conjugate harmonic functions, orthogonal harmonic functions, martingale, orthogonal martingales, norm inequality, optimal stopping problem
Categories:31B05, 60G44, 60G40

3. CMB 2004 (vol 47 pp. 481)

Bekjan, Turdebek N.
A New Characterization of Hardy Martingale Cotype Space
We give a new characterization of Hardy martingale cotype property of complex quasi-Banach space by using the existence of a kind of plurisubharmonic functions. We also characterize the best constants of Hardy martingale inequalities with values in the complex quasi-Banach space.

Keywords:Hardy martingale, Hardy martingale cotype,, plurisubharmonic function
Categories:46B20, 52A07, 60G44

4. CMB 1999 (vol 42 pp. 321)

Kikuchi, Masato
Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces
We shall study some connection between averaging operators and martingale inequalities in rearrangement invariant function spaces. In Section~2 the equivalence between Shimogaki's theorem and some martingale inequalities will be established, and in Section~3 the equivalence between Boyd's theorem and martingale inequalities with change of probability measure will be established.

Keywords:martingale inequalities, rearrangement invariant function spaces
Categories:60G44, 60G46, 46E30

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