Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1988-0943090-4
MathSciNet review: 943090
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [L] Breiman (1968), Probability, Addison-Wesley, Reading, Mass. MR 0229267 (37:4841)
  • [W] Feller (1971), An introduction to probability theory and its applications. II, 2nd ed., Wiley, New York.
  • [T] Lindvall (1977), A probabilistic proof of Blackwell's renewal theorem, Ann. Prob. 5, 482-485. MR 0440726 (55:13597)
  • [L] A. Shepp (1964), A local limit theorem, Ann. Math. Statist. 35, 419-423. MR 0166817 (29:4090)
  • [C] J. Stone (1965), A local limit theorem for multidimensional distribution functions, Ann. Math. Statist. 36, 546-551. MR 0175166 (30:5351)
  • 1. -(1967), On local and ratio limit theorems, Proc. Fifth Berkeley Sympos. Math. Statist. and Prob., vol. II, pp. 217-224, Univ. of California Press, Berkeley, Calif. MR 0222939 (36:5989)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60J15, 60F99, 60G50

Retrieve articles in all journals with MSC: 60J15, 60F99, 60G50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0943090-4
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society