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Anna Rita Sambucini

Publications and source records attributed to Anna Rita Sambucini.

36 records · Page 2Linked to original sources
arXiv2019

A Girsanov Result through Birkhoff Integral

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.

math.FA↗
arXiv2019

Properties of the Riemann-Lebesgue integrability in the non-additive case

We study Riemann-Lebesgue integrability of a vector function relative to an arbitrary non-negative set function. We obtain some classical integral properties. Results regarding the continuity properties of the integral and relationships among Riemann-Lebesgue, Birkhoff simple and Gould integrabilities are also established.

math.FA↗
arXiv2016

$L^p$ spaces in vector lattices and applications

$L^p$ spaces are investigated for vector lattice-valued functions, with respect to filter convergence. As applications, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian Motion and the Brownian Bridge are studied, to solve some stochastic differential equations.

math.FA↗
arXiv2016

Atomicity related to non-additive integrability

In this paper we present some results concerning Gould integrability of vector functions with respect to a monotone measure on finitely purely atomic measure spaces. As an application a Radon-Nikodym theorem in this setting is obtained.

math.FA↗
arXiv2015

Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures

Henstock-type integrals are considered, for multifunctions taking values in the family of weakly compact and convex subsets of a Banach lattice $X$. The main tool to handle the multivalued case is a Rådström-type embedding theorem established by C. C. A. Labuschagne, A. L. Pinchuck, C. J. van Alten in 2007. In this way the norm and order integrals reduce to that of a single-valued function taking values in an $M$-space, and new proofs are deduced for some decomposition results recently stated in two recent papers by Di Piazza and Musial based on the existence of integrable selections.

math.FA↗
arXiv2015

Set-valued Brownian motion

Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach space $X$. The present paper is an application of one the paper of the second author in which an embedding result is obtained which considers also the ordered structure of $ck(X)$ and f-algebras.

math.FA↗
arXiv2015

A note on set-valued Henstock--McShane integral in Banach (lattice) space setting

We study Henstock-type integrals for functions defined in a Radon measure space and taking values in a Banach lattice $X$. Both the single-valued case and the multivalued one are considered (in the last case mainly $cwk(X)$-valued mappings are discussed). The main tool to handle the multivalued case is a Rådström-type embedding theorem established in [50]: in this way we reduce the norm-integral to that of a single-valued function taking values in an $M$-space and we easily obtain new proofs for some decomposition results recently stated in [33,36], based on the existence of integrable selections. Also the order-type integral has been studied: for the single-valued case some basic results from [21] have been recalled, enlightning the differences with the norm-type integral, specially in the case of $L$-space-valued functions; as to multivalued mappings, a previous definition ([6]) is restated in an equivalent way, some selection theorems are obtained, a comparison with the Aumann integral is given, and decompositions of the previous type are deduced also in this setting. Finally, some existence results are also obtained, for functions defined in the real interval $[0,1]$.

math.FA↗
arXiv2015

An extension of the Birkhoff integrability for multifunctions

A comparison between a set-valued Gould type and simple Birkhoff integrals of $bf(X)$-valued multifunctions with respect to a non-negative set functionis given. Relationships among them and Mc Shane multivalued integrability is given under suitable assumptions.

math.FA↗
arXiv2015

Comparison between some norm and order gauge integrals in Banach lattices

Henstock-type integrals are considered, for functions defined in a Radon measure space and taking values in a Banach lattice X considering the norm and the order structure of the space. A number of results are obtained, highlighting the differences between them, specially in the case of L-space-valued functions.

math.FA↗
arXiv2014

Filter convergence and decompositions for vector lattice-valued measures

Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $σ$-additive case is studied, without particular assumptions on the filter; later the finitely additive case is faced, first assuming uniform $s$-boundedness (without restrictions on the filter), then relaxing this condition but imposing stronger properties on the filter. In order to obtain the last results, a Schur-type convergence theorem is used.

math.FA↗