Random mappings on infinite dimensional spaces

Thang, Dang Hung

doi:10.1080/17442509808834157

Cited by 9 publications

(9 citation statements)

References 9 publications

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“…We shall mention further how several such concepts from the scientific literature fit in our present setting. When Λ is a separable metric space (which can automatically be regarded as a measurable space with respect to a positive measure on the σ-algebra Σ = BorΛ of Borel sets), then we find ourself with multivariate stochastic mappings in the framework of infinite dimensional random mappings from the paper [25]. Let us mention that in this framework regularity conditions (some kinds of continuity or measurability) for m. [15], [5]).…”

Section: Preliminaries and Basic Notationsmentioning

confidence: 97%

Stochastic mappings and random distribution fields: A correlation approach

Gaşpar

Popa

2018

Monatsh Math

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This paper contains a study of multivariate second order stochastic mappings indexed by an abstract set Λ in close connection to their operator covariance functions. The characterizations of the normal Hilbert module or of Hilbert spaces associated to such a multivariate second order stochastic mapping in terms of reproducing kernel structures are given, aiming not only to gather into a unified way some concepts from the field, but also to indicate an instrument for extending the very well elaborated theory of multivariate second order stochastic processes (or random fields) to the case of multivariate second order random distribution fields, including multivariate second order stochastic measures. In particular a general Wold type decomposition is extended and discussed in our framework.

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Section: Preliminaries and Basic Notationsmentioning

confidence: 97%

Stochastic mappings and random distribution fields: A correlation approach

Gaşpar

Popa

2018

Monatsh Math

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“…In quite recent times, the study of stochastic processes or random fields was enlarged to the framework of multivariate stochastic mappings (see [2,20]) in order to treat in a unified way also other probabilistic concepts such as stochastic measures and stochastic integrals, random distributions or random distribution fields, as well as random operators (see [3][4][5]7,8,15,[17][18][19][20][21][22]), but also in an attempt to develop in this setting a corresponding random spectral theory (see [7,8,15,18,24,25]). B Pȃstorel Gaşpar pastorel.gaspar@uav.ro 1 Department of Mathematics and Computer Science, Faculty of Exact Sciences, "Aurel Vlaicu" University, Arad, Str.…”

Section: Introductionmentioning

confidence: 99%

“…For a study of such mappings see [19,20], for p = 0, 2 and [2][3][4] for p = 2. In this paper, we restrain ourselves to the case in which is a complex separable Hilbert space G (which can differ from H ) or some dense subspace of G. We shall call these p-order random operators.…”

Section: Introductionmentioning

confidence: 99%

On Random Normal Operators and Their Spectral Measures

Gaşpar

2018

J Theor Probab

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The main aim of this paper is to introduce and study the subclass of not necessarily continuous, normal random operators, establishing connections with other subclasses of random operators, as well as with the existing concept of random projection operatorvalued measure. Hence, after recalling some basic facts regarding random operators on a complex separable Hilbert space, theorems about transforming the class of not necessarily continuous decomposable random operators into the class of purely contractive random operators are proved. These are applied to obtain integral representations for not necessarily continuous normal or self-adjoint random operators on a Hilbert space with respect to the corresponding random projection operator-valued measures.

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“…Research in theory of random mappings has been carried out in many directions including random linear mappings which provide a framework of stochastic integral, infinite random matrix (see e.g. [2,5,11], [14][15][16][17][18][19]), random fixed points of random operators, semi groups of random operators and random operator equations (e.g. [3], [6], [10]- [16] and references therein).…”

Section: Introduction mentioning

confidence: 99%

“…which is linear and bounded is called a random linear bounded operator (see [11,14,15,17]) and a generalized random mapping…”

Section: Introduction mentioning

confidence: 99%

Bounded generalized random linear operators

Thinh¹

2017

MaP

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In this paper we are concerned with bounded generalized random linear operators. It is shown that each bounded generalized random linear operator can be seen as a set-valued random variable. The properties of some special bounded generalized random linear operators are given also. As an application the notion of random resolvent set of a generalized random linear operator is introduced and investigated.

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Random mappings on infinite dimensional spaces

Cited by 9 publications

References 9 publications

Stochastic mappings and random distribution fields: A correlation approach

Stochastic mappings and random distribution fields: A correlation approach

On Random Normal Operators and Their Spectral Measures

Bounded generalized random linear operators

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