On strong and almost sure local limit theorems for a probabilistic model of the Dickman distribution

Let { Z k } k  ≥ 1 denote a sequence of independent Bernoulli random variables defined by P ( Z k = 1) = 1 /k = 1 − P ( Z k = 0) ( k ≥ 1) and put T n  ≔ ∑ 1 ≤  k  ≤  n   kZ k . It is known that T n /n convergesweakly to a real random variable D with density proportional to the Dickman function, defi...

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Veröffentlicht in:	Lithuanian mathematical journal 2021-07, Vol.61 (3), p.301-311
Hauptverfasser:	de la Bretèche, Régis, Tenenbaum, Gérald
Format:	Artikel
Sprache:	eng
Schlagworte:	Actuarial Sciences Differential equations Independent variables Mathematics Mathematics and Statistics Number Theory Ordinary Differential Equations Probabilistic models Probability Probability Theory and Stochastic Processes Random variables Theorems
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