ISSN:
1573-8795
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract One considers the weighted sums $$S(\alpha (\delta )) = \sum\limits_{k = 0}^\infty {\alpha _k (\delta )} X_k$$ , where Xk, are independent random variables, having no densities, and αk(δ) are nonnegative functions, defined on the interval (0, 1). One investigates the conditions under which S(α(δ)) has a density; one proves a local limit theorem; one studies the form of the distribution in the case when α(δ)=δk and the variables Xk take only a finite number of values.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01093822
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