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In this paper, the precise asymptotic behaviour of the large deviation probability is found in the case where the random variables are attracted to a non-normal stable law. This extends previous work of the same author in which only the order of magnitude of the large deviation probability was found.
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Feller, W. (1966) : An Introduction to Probability Theory and its Applications, Vol. II, Wiley, New York.
Gnedenko, B. V. and Kolmogorov, A. N. (1954) : Limit Distributions for Sums of Independent Random Variables, Translated and annotated by K. L. Chung, Addison Wesley, Cambridge (Mass.).
Heyde, C. C. (1967a): A contribution to the theory of large deviations for sums of independent random variables. Z. Wahrscheinlichkeitstheorie, 7, 303–308.
Heyde, C. C. (1967b) : On large deviation problems for sums of random variables which are not attracted to the normal law. Ann. Math. Stat., 38, 1575–1578.
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Paper received: June, 1967.
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Heyde, C.C. (2010). On Large Deviation Probabilities in the Case of Attraction to a Non-Normal Stable Law. In: Maller, R., Basawa, I., Hall, P., Seneta, E. (eds) Selected Works of C.C. Heyde. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5823-5_13
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DOI: https://doi.org/10.1007/978-1-4419-5823-5_13
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