PROBABILITY DISTRIBUTIONS RELATED TO THE LAW OF THE ITERATED LOGARITHM

AUTOR(ES)

Robbins, H.

RESUMO

Let W(t) denote a standard Wiener process for 0 ≤ t < ∞. We compute the probability that W(t) ≥ t½ A(t) for some t ≥ 1 (or for some t ≥ 0) for a certain class of functions A(t), including functions which are ∼ (2 log log t)½ as t → ∞. We also give an invariance principle which states that this probability is the limit as m → ∞ of the probability that sn ≥ n½ A(n/m) for some n ≥ m (or for some n ≥ 1), where sn is the sum of n independent and identically distributed random variables with mean 0 and variance 1.

Documentos Relacionados

• ON THE LAW OF THE ITERATED LOGARITHM*
• On the other law of the iterated logarithm for self-normalized sums
• ON THE LAW OF THE ITERATED LOGARITHM WITHOUT ASSUMPTIONS ABOUT THE EXISTENCE OF MOMENTS*
• ITERATED LOGARITHM INEQUALITIES*
• Probability Distributions and Compartment Boundaries in the Development of Drosophila