| 1. |
- Abola, Benard, 1971-, et al.
(författare)
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PageRank in evolving tree graphs
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 ; , s. 375-390
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Bokkapitel (refereegranskat)abstract
- In this article, we study how PageRank can be updated in an evolving tree graph. We are interested in finding how ranks of the graph can be updated simultaneously and effectively using previous ranks without resorting to iterative methods such as the Jacobi or Power method. We demonstrate and discuss how PageRank can be updated when a leaf is added to a tree, at least one leaf is added to a vertex with at least one outgoing edge, an edge added to vertices at the same level and forward edge is added in a tree graph. The results of this paper provide new insights and applications of standard partitioning of vertices of the graph into levels using breadth-first search algorithm. Then, one determines PageRanks as the expected numbers of random walk starting from any vertex in the graph. We noted that time complexity of the proposed method is linear, which is quite good. Also, it is important to point out that the types of vertex play essential role in updating of PageRank.
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| 2. |
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| 3. |
- Biganda, Pitos, 1981-, et al.
(författare)
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Traditional and lazy pageranks for a line of nodes connected with complete graphs
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 ; , s. 391-412
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Bokkapitel (refereegranskat)abstract
- PageRank was initially defined by S. Brin and L. Page for the purpose of measuring the importance of web pages (nodes) based on the structure of links between them. Due to existence of diverse methods of random walk on the graph, variants of PageRank now exists. They include traditional (or normal) PageRank due to normal random walk and Lazy PageRank due to lazy random walk on a graph. In this article, we establish how the two variants of PageRank changes when complete graphs are connected to a line of nodes whose links between the nodes are in one direction. Explicit formulae for the two variants of PageRank are presented. We have noted that the ranks on a line graph are the same except their numerical values which differ. Further, we have observed that both normal random walk and lazy random walk on complete graphs spend almost the same time at each node.
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| 4. |
- Lindensjö, Kristoffer, 1979-
(författare)
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Constructive martingale representation in functional Itô calculus : a local martingale extension
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028251 - 9783030028244 ; , s. 165-172
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Bokkapitel (refereegranskat)abstract
- The constructive martingale representation theorem of functional Itô cal-culus is extended, from the space of square integrable martingales, to the space of local martingales. The setting is that of an augmented filtration generated by a Wiener process.
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| 5. |
- Malyarenko, Anatoliy, 1957-, et al.
(författare)
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Random fields related to the symmetry classes of second-order symmetric tensors
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 ; , s. 173-185
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Bokkapitel (refereegranskat)abstract
- Under the change of basis in the three-dimensional space by means of an orthogonal matrix g, a matrix A of a linear operator is transformed as A → gAg-1 Mathematically, the stationary subgroup of a symmetric matrix under the above action can be either (Formula Presented), when all three eigenvalues of A are different, or (Formula Presented), when two of them are equal, or O(3), when all three eigenvalues are equal. Physically, one typical application relates to dependent quantities like a second-order symmetric stress (or strain) tensor. Another physical setting is that of dependent fields, such as conductivity with such three cases is the conductivity (or, similarly, permittivity, or anti-plane elasticity) second-rank tensor, which can be either orthotropic, transversely isotropic, or isotropic. For each of the above symmetry classes, we consider a homogeneous random field taking values in the fixed point set of the class that is invariant with respect to the natural representation of a certain closed subgroup of the orthogonal group. Such fields may model stochastic heat conduction, electric permittivity, etc. We find the spectral expansions of the introduced random fields.
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| 6. |
- Silvestrov, Dmitrii, 1947-
(författare)
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A journey in the word of stochastic processes
- 2018
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Ingår i: Stochastic processes and applications. - Cham : Springer. - 9783030028244 - 9783030028251 ; , s. 7-21
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Bokkapitel (refereegranskat)abstract
- This paper presents a survey of research results obtained by the authorand his collaborators in the areas of limit theorems for Markov-type processes andrandomly stopped stochastic processes, renewal theory and ergodic theorems forperturbed stochastic processes, quasi-stationary distributions for perturbed stochas-tic systems, methods of stochastic approximation for price processes, asymptoticexpansions for nonlinearly perturbed semi-Markov processes and applications ofthe above results to queuing systems, reliability models, stochastic networks, bio-stochastic systems, perturbed risk processes, and American-type options.
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| 7. |
- Silvestrov, Dmitrii, 1947-
(författare)
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Individual ergodic theorem for perturbed alternating regenerative processes
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 - 9783030028251 ; , s. 23-89
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Bokkapitel (refereegranskat)abstract
- The paper presents results of complete analysis and classification of individual ergodic theorems for perturbed alternating regenerative processes with semi-Markov modulation. New short, long and super-long time ergodic theorems for regularly and singular type perturbed alternating regenerative processes are presented.
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| 8. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
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Nonlinearly perturbed birth-death-type models
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 - 9783030028251 ; , s. 189-244
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Bokkapitel (refereegranskat)abstract
- Asymptotic expansions are presented for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov models, as well as algorithms for computing the coefficients of these expansions. Three types of applications are discussed in detail. The first is a model of population growth, where either an isolated population is perturbed by immigration, or a sink population with immigration is perturbed by internal births. The second application is epidemic spread of disease, in which a closed population is perturbed by infected individuals from outside. The third model captures the time dynamics of the genetic composition of a population with genetic drift and selection, that is perturbed by various mutation scenarios.
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| 9. |
- Silvestrov, Sergei, Professor, 1970-, et al.
(författare)
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Dmitrii S. Silvestrov
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 ; , s. 1-4
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Bokkapitel (refereegranskat)abstract
- This chapter presents short biographical notes about Professor Dmitri S. Silvestrov.
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| 10. |
- Silvestrov, Sergei, Professor, 1970-, et al.
(författare)
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Preface
- 2018
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Ingår i: Stochastic Processes and Applications. - : Springer. - 9783030028244 - 9783030028251 ; , s. vii-x
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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