Generalized Random Spectral Measures

Thang, Dang Hung; Thinh, Nguyen An; Quy, Tran Xuan

doi:10.1007/s10959-012-0461-0

Cited by 9 publications

(49 citation statements)

References 12 publications

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“…Let us mention that in this framework regularity conditions (some kinds of continuity or measurability) for m. [15], [5]). Also covered by this concept are the stochastic or random measures (see [27]), stochastic or random integrals and the random operators (see [25, pp. 54, 55]).…”

Section: Preliminaries and Basic Notationsmentioning

confidence: 99%

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: 99%

Stochastic mappings and random distribution fields: A correlation approach

Gaşpar

Popa

2018

Monatsh Math

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“…In this section, some definitions and typical results on random bounded operator, bounded generalized random linear operator are listed and discussed. For more details, we refer the reader to [14,17,18,19].…”

Section: Random Bounded Operators and Bounded Generalized Random Linementioning

confidence: 99%

“…Noting that the exceptional set in (1) may depend on x.A random bounded operator is a random operator but in general, a random operator needs not be bounded. For examples of random operators, random bounded operators and unbounded random bounded operators, we refer to [14,17,19]. It is easy to prove the following Theorem which is a little bit more general than a result in [17].…”

Section: Random Bounded Operators and Bounded Generalized Random Linementioning

confidence: 99%

“…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%

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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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“…Research in theory of random operators has been carried out in many directions including random linear operators which provide a framework of stochastic integral, infinite random matrix (see e.g. [1], [2], [15]- [20], [23]- [26]), random fixed points of random operators and random operator equations, (e.g [3]- [14], [18], [21], [22] and references therein). As an extension of random linear operators, generalized random linear operators on a separable Hilbert space were introduced and investigated in [25].…”

Section: Introductionmentioning

confidence: 99%