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 Mathematics

Technion-Israel Institute of Technology

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

3 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	Funder number
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",

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year = "1986",

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AU - Zakai, Moshe

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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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Bimeasures and measures induced by planar Stochastic integrators

Abstract

Bibliographical note

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Keywords

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