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

DOI: 10.4213/tvp608

 English version: Theory of Probability and its Applications, 2000, 44:1, 131–135

Bibliographic databases:

• 
• 
•