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Series representation of time-stable stochastic processes

100%

Kopp C. , Molchanov I.

Probability and Mathematical Statistics

2018

tom Vol. 38, Fasc. 2

299--315

A stochastically continuous process ξ(t), t ≥ 0, is said to be time-stable if the sum of n i.i.d. copies of ξ equals in distribution the time-scaled stochastic process ξ(nt), t ≥ 0. The paper advances the understanding of time-stable processes by means of their LePage series representations as the sum of i.i.d. processes with the arguments scaled by the sequence of successive points of the unit intensity Poisson process on [0,∞). These series yield numerous examples of stochastic processes that share one-dimensional distributions with a Lévy process.

XML documents change detection system based on boolean linear programming task

80%

Globa L. , Alieksieiev M. , Molchanov I.

Metody Informatyki Stosowanej

2011

tom nr 2

25-35

This paper describes the main ideas of XML change detection system which is based on developed linear programming algorithm for XML change detection. The linear programming algorithm for XML change detection is developed to compare the trees of old web page and modified web page to find the changes between them. The approach presented in this paper differs from the previously cited ones. The first main idea of proposed algorithm is in paying attention only to quantitative changes in the tracked documents, instead of searching the exact changes sequence that produces the new document. The second main idea is in comparison of two document versions as if they are different documents. Such approach doesn’t need the reference map between XML tags of two documet versions. The proposed technique represents the change detection problem as the Boolean linear programming task and proposes effective solution method.