An Alberti's rank-one theorem for martingales

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An Alberti's rank-one theorem for martingales. / Ayoush, Rami; Столяров, Дмитрий Михайлович; Wojciechowski, Michał.

In: Pacific Journal of Mathematics, Vol. 334, No. 1, 2025.

Research output: Contribution to journal › Article › peer-review

Author

Ayoush, Rami ; Столяров, Дмитрий Михайлович ; Wojciechowski, Michał. / An Alberti's rank-one theorem for martingales. In: Pacific Journal of Mathematics. 2025 ; Vol. 334, No. 1.

BibTeX

@article{3d5b67963ec8444183bb386c074cf281,

title = "An Alberti's rank-one theorem for martingales",

abstract = "We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the q-regular filtration. This dependency is governed by a martingale analog of the so-called wave cone, which naturally corresponds to the result of De Philippis and Rindler about fine properties of PDE-constrained vector measures. As a corollary we obtain a martingale version of Alberti{\textquoteright}s rank-one theorem.",

keywords = "martingale, rank-one property, vector measure",

author = "Rami Ayoush and Столяров, {Дмитрий Михайлович} and Micha{\l} Wojciechowski",

year = "2025",

doi = "10.2140/pjm.2025.334.1",

language = "English",

volume = "334",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California Press",

number = "1",

}

RIS

TY - JOUR

T1 - An Alberti's rank-one theorem for martingales

AU - Ayoush, Rami

AU - Столяров, Дмитрий Михайлович

AU - Wojciechowski, Michał

PY - 2025

Y1 - 2025

N2 - We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the q-regular filtration. This dependency is governed by a martingale analog of the so-called wave cone, which naturally corresponds to the result of De Philippis and Rindler about fine properties of PDE-constrained vector measures. As a corollary we obtain a martingale version of Alberti’s rank-one theorem.

AB - We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the q-regular filtration. This dependency is governed by a martingale analog of the so-called wave cone, which naturally corresponds to the result of De Philippis and Rindler about fine properties of PDE-constrained vector measures. As a corollary we obtain a martingale version of Alberti’s rank-one theorem.

KW - martingale

KW - rank-one property

KW - vector measure

UR - https://www.mendeley.com/catalogue/257836b9-e8a0-37e9-bc60-cd9462334627/

U2 - 10.2140/pjm.2025.334.1

DO - 10.2140/pjm.2025.334.1

M3 - Article

VL - 334

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -

ID: 134719756