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Short Communications
Local limit theorems for conditionally independent random variables controlled by a finite Markov chain
T. Shervashidze A. Razmadze Mathematical Institute, Georgian Academy of Sciences
Abstract:
The sufficient conditions for the validity of local theorems for conditionally independent random variables controlled by a finite homogeneous regular Markov chain are given in terms of conditional distributions of summands.
Keywords:
conditionally independent random variables, local theorems for densities, local theorem for lattice distributions, normal attraction to the stable law.
Received: 24.07.1997
Citation:
T. Shervashidze, “Local limit theorems for conditionally independent random variables controlled by a finite Markov chain”, Teor. Veroyatnost. i Primenen., 44:1 (1999), 143–148; Theory Probab. Appl., 44:1 (2000), 131–135
Linking options:
https://www.mathnet.ru/eng/tvp608https://doi.org/10.4213/tvp608 https://www.mathnet.ru/eng/tvp/v44/i1/p143
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