Generalized sub-Gaussian fractional Brownian motion queueing model

Yamnenko, Rostyslav; Kozachenko, Yuriy; Bushmitch, D.

doi:10.1007/s11134-013-9375-5

Cited by 9 publications

(7 citation statements)

References 14 publications

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“…The developed methodology and new estimates are important extensions of the known results in the stochastic sampling theory to the space L p ([0, T ]) and the class of ϕ-sub-Gaussian random processes. In addition to classical applications of ϕ-sub-Gaussian random processes in signal processing, the results can also be used in new areas, for example, compressed sensing and actuarial modelling, see, e.g., [18,39,40].…”

Section: Discussionmentioning

confidence: 99%

Whittaker–Kotel'nikov–Shannon approximation of φ-sub-Gaussian random processes

Kozachenko

Olenko

2016

Journal of Mathematical Analysis and Applications

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The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates L p ([0, T ]) and uniform approximations of ϕ-sub-Gaussian random processes by finite time sampling sums. Explicit truncation error upper bounds are established. Some specifications of the general results for which the assumptions can be easily verified are given. Direct analytical methods are employed to obtain the results.

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Section: Discussionmentioning

confidence: 99%

Whittaker–Kotel'nikov–Shannon approximation of φ-sub-Gaussian random processes

Kozachenko

Olenko

2016

Journal of Mathematical Analysis and Applications

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“…This class plays an important role in generalizations of various theoretical properties of Gaussian processes. In addition to classical applications of ϕ-sub-Gaussian random processes in signal processing, the results can also be used in new areas, like compressed sensing and actuarial modelling, consult, for example, Labate et al 2013, Vershynin 2012, Yamnenko 2006 It would be of interest to adopt and specify the results for different wavelet bases, which satisfy the assumptions of the theorems, for example, Daubechies, Battle-Lemarie and Meyer wavelets; -to examine the tightness of the estimates by simulations.…”

Section: Discussionmentioning

confidence: 99%

Convergence in L p ([0, T]) of Wavelet Expansions of φ-Sub-Gaussian Random Processes

Kozachenko

Olenko

Polosmak

2013

Methodol Comput Appl Probab

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“…Note that condition (46) holds, in particular, for the (Gaussian) fractional Brownian motion with the corresponding Hurst index H. More details on the generalized fractional Brownian motion belonging to the classes V (ϕ, ψ) are given in the papers [3,6,8].…”

Section: X(t) = {X(t) T ∈ B}mentioning

confidence: 99%

Bounds for the distribution of some functionals of processes with $\varphi $-sub-Gaussian increments

Yamnenko

2013

Theor. Probability and Math. Statist.

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Abstract. Bounds for the distribution of some functionals of a stochastic process {X(t), t ∈ T } belonging to the class V (ϕ, ψ) are obtained. An example of the functionals studied in the paper is given bywhere f (t) is a continuous function that can be viewed as a service output rate of a queue formed by the process X(t). For the latter interpretation, the bounds can be viewed as upper estimates for the buffer overflow probabilities with buffer size x > 0. The results obtained in the paper apply to Gaussian stochastic processes. As an example, we show an application for the generalized fractional Brownian motion defined on a finite interval.

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Generalized sub-Gaussian fractional Brownian motion queueing model

Cited by 9 publications

References 14 publications

Whittaker–Kotel'nikov–Shannon approximation of φ-sub-Gaussian random processes

Whittaker–Kotel'nikov–Shannon approximation of φ-sub-Gaussian random processes

Convergence in L p ([0, T]) of Wavelet Expansions of φ-Sub-Gaussian Random Processes

Bounds for the distribution of some functionals of processes with $\varphi $-sub-Gaussian increments

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