DOI
10.34229/KCA2522-9664.25.5.14
UDC 519.217
O.A. Yarova
Ivan Franko National University of Lviv, Lviv, Ukraine,
oksana.yarova@lnu.edu.ua,
oksanayarova93@gmail.com
ASYMPTOTICS OF THE MULTIDIMENSIONAL SOLUTION
FOR RENEWAL EQUATION
Abstract. This paper considers the multidimensional renewal equation in matrix form. The asymptotics of the renewal equation with a nonlinear normalization factor are found. The theorem on the asymptotics of the multidimensional renewal equation is proved.
Keywords: renewal equation, renewal function, process with independent increments, weak convergence.
full text
REFERENCES
- 1. Yarova O.A., Yeleyko Ya.I. Limit theorem for multidimensional renewal equation. Cybernetics and Systems Analysis. 2022. Vol. 58, N 1. P. 144–147. https://doi.org/10.1007/s10559-022-00443-4.
- 2. Yeleyko Ya.I., Nishchenko I.I. On an asymptotic representation of the Perror root of a matrix-valued evolution. Ukrain. Mat. Zh. 1996. Vol. 48, N 1. P. 35–43.
- 3. Feller W. A simple proof for renewal theorems. Communs Pure and Appl. Math. 1961. N 14. P. 285–293.
- 4. Yarova O.A., Yeleyko Ya.I. The renewal equation in nonlinear approximation. Matematychni Studii. 2021. Vol. 56, N 1. P. 103–106. https://doi.org/10.30970/ms.56.1.103-106.
- 5. Yeleyko Ya.I., Nishchenko I.I. A limit theorem for a matrix-valued evolution. Вісник ЛНУ. Cер. мех.-мат. 1993. Vol. 53. С. 102–107.