Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions

Candeloro, Domenico; Piazza, L. Di; Musiał, Kazimierz; Sambucini, Anna Rita

doi:10.1007/s10231-017-0674-z

Cited by 21 publications

(20 citation statements)

References 35 publications

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“…Using this result we are able to observe that Proposition 3.7. Let w t be a Brownian motion and N the vector measure defined in (5) . Then for every s < t it is…”

Section: A Girsanov Resultsmentioning

confidence: 99%

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A Girsanov Result Through Birkhoff Integral

Candeloro

Sambucini

2018

Computational Science and Its Applications – ICCSA 2018

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A vector-valued version of the Girsanov theorem is presented, for a scalar process with respect to a Banach-valued measure. Previously, a short discussion about the Birkhoff-type integration is outlined, as for example integration by substitution, in order to fix the measure-theoretic tools needed for the main result, Theorem 6, where a martingale equivalent to the underlying vector probability has been obtained in order to represent the modified process as a martingale with the same marginals as the original one.

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“…Using this result we are able to observe that Proposition 3.7. Let w t be a Brownian motion and N the vector measure defined in (5) . Then for every s < t it is…”

Section: A Girsanov Resultsmentioning

confidence: 99%

“…Denoted by Φ(ω) := E (•|w T (ω)), the measure N : A → X defined in(5) satisfies the following equality:N (A) = A Φ (ω) dP(ω) = A E (•|w T (ω)) dP(ω) So, thanks to Proposition 2.11, it is A φ(ω)dN (ω) = A φ(ω)Φ(ω)dP(ω) = A E (φ(ω)|w T (ω)) dP(ω).…”

mentioning

confidence: 99%

A Girsanov Result Through Birkhoff Integral

Candeloro

Sambucini

2018

Computational Science and Its Applications – ICCSA 2018

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“…Moreover by [18] (Theorem 6.6) vH-integrability and vH integrability coincide. In all the cases Φ Γ : I → cwk(X) is an additive interval multimeasure.…”

Section: Now We Recall Here Briefly the Definitions Of The Integrals Involved In This Article A Scalarly Integrable Multifunctionmentioning

confidence: 88%

Decompositions of Weakly Compact Valued Integrable Multifunctions

Piazza

Musiał

2020

Mathematics

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We give a short overview on the decomposition property for integrable multifunctions, i.e., when an “integrable in a certain sense” multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it starting from the seminal paper of the authors in 2006, where the property was proved for Henstock integrable multifunctions taking compact convex values in a separable Banach space X. In this paper, we summarize the earlier results, we prove further results and present tables which show the state of art in this topic.

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“…The vector ν(E) is then called the Pettis integral of f over E and we set ν(E) = (P ) E f dλ. We refer to [3], [17]- [19], [22] and [2] for Pettis integral.…”

Section: Replacing the Last Inequality Withmentioning

confidence: 99%

Some remarks on descriptive characterizations of the strong McShane integral

Kaliaj¹

2018

Math.Boh.

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We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function f : W → X defined on a non-degenerate closed subinterval W of R m in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure V M F generated by the primitive F : I W → X of f , where I W is the family of all closed non-degenerate subintervals of W .

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Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions

Cited by 21 publications

References 35 publications

A Girsanov Result Through Birkhoff Integral

A Girsanov Result Through Birkhoff Integral

Decompositions of Weakly Compact Valued Integrable Multifunctions

Some remarks on descriptive characterizations of the strong McShane integral

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