Nishchenko I. Transition phenomena of many-dimensional renewal theory and it applications to the investigation of the asymptotic properties of random evolutions

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0402U001858

Thesis Registration Form

0402U001858.pdf

Applicant for

Specialization

  • 01.01.05 - Теорія ймовірностей і математична статистика

11-06-2002

Specialized Academic Board

Д 26.206.02

The Institute of Mathematics of NASU

Essay

Main results of the classical renewal theory is generalized to the class of many-dimensional renewal equations in the scheme of series built upon the family of depending upon a small parameter matrix-valued measures with the block-diagonal full measure matrix. Asymptotic behaviour of matrix-valued renewal function and solution of the renewal equation of mentioned above kind are investigated as the time argument tends to infinity and the series parameter tends to zero. The theorem of averaging in a scheme of asymptotic phase marging for semi- Markov random evolution and theorem of averaging for evolution given by the transport equation on the regenerative process are proved.

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