Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
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Andrey M. Zubkov
und
Maksim P. Savelov
Abstract
It is shown that, with suitable time change, the finite-dimensional distributions of the process formed by successive values of the Pearson statistics for an expanding sample converge to finite-dimensional distributions of the stationary random process, namely, the normalized square of the Bessel process. The results obtained earlier on the limit joint distributions of the Pearson statistics are used to derive explicit formulas for the density of joint distributions of the Bessel process.
Originally published in Diskretnaya Matematika (2016) 28, №3, 49–58 (in Russian).
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© 2017 Walter de Gruyter GmbH Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Estimating the level of affinity of a quadratic form
- Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
- Large deviations of branching processes with immigration in random environment
- On the probability of existence of substrings with the same structure in a random sequence
- Linearly realizable automata
- On the number of labeled outerplanar k-cycle blocks
- Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
Artikel in diesem Heft
- Frontmatter
- Estimating the level of affinity of a quadratic form
- Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
- Large deviations of branching processes with immigration in random environment
- On the probability of existence of substrings with the same structure in a random sequence
- Linearly realizable automata
- On the number of labeled outerplanar k-cycle blocks
- Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
