On the convergence of the product of independent random operators

Thang, Dang Hung; Son, Ta Cong

doi:10.1080/17442508.2016.1172579

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…The interest in random operators has been arouse not only for its own right but also for their widespread applications in other areas ( [11]). Some results on random operators can be found in [3,11,13,14,15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

On the regularity of generalized random spectral measures and their applications

Nguyen¹,

Hung²,

Cong³

2022

Preprint

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This paper is devoted to the regularity of generalized random spectral measures. First, we prove that every generalized random spectral measure defined on a locally compact metric space with values in a separable Hilbert space is regular. A solution of the Schrödinger-type random equation is obtained as an application. In the second part of this paper, we show that every finitely additive generalized random spectral measure defined on an arbitrary measurable space with values in a finite-dimensional Hilbert space is also regular. In addition, an random version of Jordan’s classical decomposition theorem for a matrix is provided. Subject Classification. Primary 60H25; Secondary 46G10, 60B11, 45R05.

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Section: Introductionmentioning

confidence: 99%

On the regularity of generalized random spectral measures and their applications

Nguyen¹,

Hung²,

Cong³

2022

Preprint

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“…The random operator theory is one of the branches of the theory of random processes and functions; its creation is a natural step in the development of random analysis. Research in theory of random operators has been carried out in many directions such as random fixed points of random operators, random operator equations, random linear operators (see [1][2][3][4]).…”

Section: Introductionmentioning

confidence: 99%

“…The study of the asymptotic behavior of the products of random matrices is of very importance in the analysis of the limiting behavior of solutions of systems of differential and difference equations with random coefficients (see [9] and references therein). Recently, Thang and Son [2] obtained the convergence of the products of random linear operators { } and { } of the form…”

Section: Introductionmentioning

confidence: 99%