Abstract
Of paramount concern in probability theory is the behavior of sums {S n , n ≥ 1} of independent random variables {X i, i ≥ 1}. The case where the {X i} are i.i.d. is of especial interest and frequently lends itself to more incisive results. The sequence of sums {S n, n ≥ 1} of i.i.d. r.v.s {X n} is alluded to as a random walk; in the particular case when the component r.v.s {X n} are nonnegative, the random walk is referred to as a renewal process.
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Chow, Y.S., Teicher, H. (1988). Sums of Independent Random Variables. In: Probability Theory. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0504-0_5
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