Linear recurrent relations, power series distributions, and generalized allocation scheme
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Aleksandr N. Timashev
Abstract
We consider distributions of the power series type determined by the generating functions of sequences satisfying linear recurrence relations with nonnegative coefficients. These functions are represented by power series with positive radius of convergence. An integral limit theorem is proved on the convergence of such distributions to the exponential distribution. For the generalized allocation scheme generated by these linear relations a local normal theorem for the total number of components is proved. As a consequence of more general results of the author, a limit theorem is stated containing sufficient conditions under which the distributions of the number of components having a given volume converge to the Poisson distribution.
Note: Originally published in Diskretnaya Matematika (2020) 32,№3, 98–112 (in Russian).
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Articles in the same Issue
- Frontmatter
- Single diagnostic tests for inversion faults of gates in circuits over arbitrary bases
- Generalized de Bruijn graphs
- A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic
- Linear recurrent relations, power series distributions, and generalized allocation scheme
- Variance of the number of cycles of random A-permutation
- Multi-dimensional Kronecker sequences with a small number of gap lengths
Articles in the same Issue
- Frontmatter
- Single diagnostic tests for inversion faults of gates in circuits over arbitrary bases
- Generalized de Bruijn graphs
- A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic
- Linear recurrent relations, power series distributions, and generalized allocation scheme
- Variance of the number of cycles of random A-permutation
- Multi-dimensional Kronecker sequences with a small number of gap lengths
