PageRank in Evolving Tree Graphs

Abola, Benard; Biganda, Pitos Seleka; Engström, Christopher; Mango, John Magero; Kakuba, Godwin; Silvestrov, Sergei

doi:10.1007/978-3-030-02825-1_16

Cited by 7 publications

(13 citation statements)

References 15 publications

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“…It is well known that, under condition A 1 , the rate of convergence in the ergodic relation (29) is exponential. This means that there exist some constants 1), and distribution π0 = π 0,j , j ∈ X , with all positive components such that the following relation holds, max…”

Section: Rate Of Convergence For Perturbed Stationary Distributionsmentioning

confidence: 99%

“…Indeed, π ε,j is a positive number, for every ε ∈ [0, 1]. Relation (54) implies that (π ε,j − π 0,j )ε −1 → π0, d,j [1] as ε → 0. Thus, π0, d,j [1] is a real number.…”

Section: Asymptotic Expansions For Perturbed Stationary Distributionsmentioning

confidence: 99%

“…Relation (54) implies that (π ε,j − π 0,j )ε −1 → π0, d,j [1] as ε → 0. Thus, π0, d,j [1] is a real number. In this way, the above proposition can be proved for all coefficients in expansions (50).…”

Section: Asymptotic Expansions For Perturbed Stationary Distributionsmentioning

confidence: 99%

“…In addition, variants of PageRank in relation to some specific networks has been studied, e.g. in [8] and [9]; and also updating PageRank due to changes in some network is in literature, for instance, in [1] and [2].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Perturbed Markov Chains and Information Networks

Abola,

Biganda,

Silvestrov

et al. 2019

Preprint

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The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, as well as explicit upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities in triangular array mode, where perturbation parameter ε → 0 and n → ∞, simultaneously. The results of numerical experiments are also presented.

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Section: Rate Of Convergence For Perturbed Stationary Distributionsmentioning

confidence: 99%

“…Indeed, π ε,j is a positive number, for every ε ∈ [0, 1]. Relation (54) implies that (π ε,j − π 0,j )ε −1 → π0, d,j [1] as ε → 0. Thus, π0, d,j [1] is a real number.…”

Section: Asymptotic Expansions For Perturbed Stationary Distributionsmentioning

confidence: 99%

Section: Asymptotic Expansions For Perturbed Stationary Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Perturbed Markov Chains and Information Networks

Abola,

Biganda,

Silvestrov

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition, variants of PageRank in relation to some specific networks has been studied, e.g. in Biganda et al (2018a, b); and also updating PageRank due to changes in some network is in literature, for instance, in Abola et al (2018a, b).…”

Section: Introductionmentioning

confidence: 99%

Perturbed Markov Chains with Damping Component

Silvestrov

Abola

et al. 2020

Methodol Comput Appl Probab

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The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, explicit coupling type upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities, as well as ergodic theorems in triangular array mode.

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