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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The influence of the initial distribution on a random walk

Author: Wolfgang Stadje
Journal: Proc. Amer. Math. Soc. 103 (1988), 602-606
MSC: Primary 60J15; Secondary 60F99, 60G50
MathSciNet review: 943090
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Abstract: Let $ {T_1},{T_2}, \ldots $ be i.i.d. random variables, $ {S_n} = {T_1} + \cdots + {T_n}$; let $ X$ and $ Y$ be independent of $ {\left( {{T_n}} \right)_{n \geq 1}}$. We study the total variation distance between the distributions of $ X + {S_n}$ and $ Y + {S_n}$, especially its speed of convergence to 0 in the case that some $ {S_j}$ is not singular.

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Article copyright: © Copyright 1988 American Mathematical Society