Geodesic
Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
Diskretnaya Matematika, Tome 28 (2016) no. 3, pp. 49-58

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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.
Keywords: Pearson statictics, sequential chi-square test, Bessel process. 
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     author = {A. M. Zubkov and M. P. Savelov},
     title = {Convergence of the sequence of the {Pearson} statistics values to the normalized square of the {Bessel} process},
     journal = {Diskretnaya Matematika},
     pages = {49--58},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_3_a4/}
}
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A. M. Zubkov; M. P. Savelov. Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process. Diskretnaya Matematika, Tome 28 (2016) no. 3, pp. 49-58. http://geodesic.mathdoc.fr/item/DM_2016_28_3_a4/