Bimeasures and measures induced by planar Stochastic integrators

Ely Merzbach; Moshe Zakai

doi:10.1016/0047-259x(86)90094-1

Bimeasures and measures induced by planar Stochastic integrators

Ely Merzbach
, Moshe Zakai

Department of General History

Technion-Israel Institute of Technology

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

4 Scopus citations

Abstract

Two parameter Stochastic processes {X_z(ω), ω ∈ Ω, z ∈ R₊²} which are L² integrators are characterized through associated bimeasures defined on the product spaces (Ω × R₊²) × (Ω × R₊²) and and Ω × R₊² × R₊². It is also shown that under further restrictions on the X process there exists an associated measure on these product spaces and X_z² possesses a Doob-Meyer-Cairoli decomposition.

Original language	English
Pages (from-to)	67-87
Number of pages	21
Journal	Journal of Multivariate Analysis
Volume	19
Issue number	1
DOIs	https://doi.org/10.1016/0047-259x(86)90094-1
State	Published - Jun 1986

Bibliographical note

Funding Information:
partly supported by the Fund for Promotion of Research at the Technion. 67

Funding

partly supported by the Fund for Promotion of Research at the Technion. 67

Funders
Technion-Israel Institute of Technology

Keywords

Doob-Meyer-Cairoli decomposition
Two-parameter stochastic integrators
bimeasures
functions of bounded variation

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10.1016/0047-259x(86)90094-1

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title = "Bimeasures and measures induced by planar Stochastic integrators",

abstract = "Two parameter Stochastic processes \{Xz(ω), ω ∈ Ω, z ∈ R+2\} which are L2 integrators are characterized through associated bimeasures defined on the product spaces (Ω × R+2) × (Ω × R+2) and and Ω × R+2 × R+2. It is also shown that under further restrictions on the X process there exists an associated measure on these product spaces and Xz2 possesses a Doob-Meyer-Cairoli decomposition.",

keywords = "Doob-Meyer-Cairoli decomposition, Two-parameter stochastic integrators, bimeasures, functions of bounded variation",

author = "Ely Merzbach and Moshe Zakai",

note = "Funding Information: partly supported by the Fund for Promotion of Research at the Technion. 67",

year = "1986",

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AU - Merzbach, Ely

AU - Zakai, Moshe

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PY - 1986/6

Y1 - 1986/6

N2 - Two parameter Stochastic processes {Xz(ω), ω ∈ Ω, z ∈ R+2} which are L2 integrators are characterized through associated bimeasures defined on the product spaces (Ω × R+2) × (Ω × R+2) and and Ω × R+2 × R+2. It is also shown that under further restrictions on the X process there exists an associated measure on these product spaces and Xz2 possesses a Doob-Meyer-Cairoli decomposition.

AB - Two parameter Stochastic processes {Xz(ω), ω ∈ Ω, z ∈ R+2} which are L2 integrators are characterized through associated bimeasures defined on the product spaces (Ω × R+2) × (Ω × R+2) and and Ω × R+2 × R+2. It is also shown that under further restrictions on the X process there exists an associated measure on these product spaces and Xz2 possesses a Doob-Meyer-Cairoli decomposition.

KW - Doob-Meyer-Cairoli decomposition

KW - Two-parameter stochastic integrators

KW - bimeasures

KW - functions of bounded variation

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JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 1

ER -

Bimeasures and measures induced by planar Stochastic integrators

Abstract

Bibliographical note

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Keywords

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