Geodesic
On convergence of distributions for sums of independent random vectors with randomly change of components
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 269-276

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We derive new results on convergence of distributions for sums of independent random vectors with randomly changed components in scheme of series. In particular, a multidimensional central limit theorem is proved. If the random change of components is defined by a Poisson process then we arrive at results on convergence of finitely dimension distributions of psi-processes. In Gaussian case, the limit process is the Ornstein–Uhlenbeck process. We discuss a replacement of the Poisson process by processes with non-negative integer increments. 
@article{ZNSL_2024_535_a17,
     author = {A. N. Frolov},
     title = {On convergence of distributions for sums of independent random vectors with randomly change of components},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {269--276},
     publisher = {mathdoc},
     volume = {535},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a17/}
}
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A. N. Frolov. On convergence of distributions for sums of independent random vectors with randomly change of components. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 269-276. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a17/