Itô-Ramer, Skorohod and Ogawa integrals with respect to Gaussian processes and their interrelationship

Leszek Gawarecki; Vidyadhar S. Mandrekar

Itô-Ramer, Skorohod and Ogawa integrals with respect to Gaussian processes and their interrelationship

Leszek Gawarecki, Vidyadhar S. Mandrekar

Kettering University

Michigan State University

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In this work, we first define Ogawa integral with respect to general Gaussian processes and we give sufficient conditions for Ogawa integrability. Under very mild conditions on the existence of "trace" of the Malliavin derivative of an Integrand, we relate the Ogawa integral to the Skorohod integral. In addition we define ltô-Ramer Integral in a very general setup and, using a generalization of a result of Gross, we give sufficient conditions for its existence. Under a differentiability condition, we give a relation between the Itô-Ramer and Skorohod integrals.

Original language	American English
Title of host publication	Chaos Expansions, Multiple Wiener-Itô Integrals, and Their Applications
State	Published - Apr 5 1994

Disciplines

Mathematics

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https://www.crcpress.com/Chaos-Expansions-Multiple-Wiener-Ito-Integrals-and-Their-Applications/Houdre-Perez-Abreu/p/book/9780849380723

Cite this

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title = "It{\^o}-Ramer, Skorohod and Ogawa integrals with respect to Gaussian processes and their interrelationship",

abstract = " In this work, we first define Ogawa integral with respect to general Gaussian processes and we give sufficient conditions for Ogawa integrability. Under very mild conditions on the existence of {"}trace{"} of the Malliavin derivative of an Integrand, we relate the Ogawa integral to the Skorohod integral. In addition we define lt{\^o}-Ramer Integral in a very general setup and, using a generalization of a result of Gross, we give sufficient conditions for its existence. Under a differentiability condition, we give a relation between the It{\^o}-Ramer and Skorohod integrals.",

author = "Leszek Gawarecki and Mandrekar, \{Vidyadhar S.\}",

year = "1994",

month = apr,

day = "5",

language = "American English",

booktitle = "Chaos Expansions, Multiple Wiener-It{\^o} Integrals, and Their Applications",

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T1 - Itô-Ramer, Skorohod and Ogawa integrals with respect to Gaussian processes and their interrelationship

AU - Gawarecki, Leszek

AU - Mandrekar, Vidyadhar S.

PY - 1994/4/5

Y1 - 1994/4/5

N2 - In this work, we first define Ogawa integral with respect to general Gaussian processes and we give sufficient conditions for Ogawa integrability. Under very mild conditions on the existence of "trace" of the Malliavin derivative of an Integrand, we relate the Ogawa integral to the Skorohod integral. In addition we define ltô-Ramer Integral in a very general setup and, using a generalization of a result of Gross, we give sufficient conditions for its existence. Under a differentiability condition, we give a relation between the Itô-Ramer and Skorohod integrals.

AB - In this work, we first define Ogawa integral with respect to general Gaussian processes and we give sufficient conditions for Ogawa integrability. Under very mild conditions on the existence of "trace" of the Malliavin derivative of an Integrand, we relate the Ogawa integral to the Skorohod integral. In addition we define ltô-Ramer Integral in a very general setup and, using a generalization of a result of Gross, we give sufficient conditions for its existence. Under a differentiability condition, we give a relation between the Itô-Ramer and Skorohod integrals.

UR - https://digitalcommons.kettering.edu/mathematics_facultypubs/16

UR - https://www.crcpress.com/Chaos-Expansions-Multiple-Wiener-Ito-Integrals-and-Their-Applications/Houdre-Perez-Abreu/p/book/9780849380723

M3 - Chapter

BT - Chaos Expansions, Multiple Wiener-Itô Integrals, and Their Applications

ER -

Itô-Ramer, Skorohod and Ogawa integrals with respect to Gaussian processes and their interrelationship

Abstract

Disciplines

Access to Document

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