law of the iterated logarithm

On the law of the iterated logarithm.

The law of the iterated logarithm provides the scaling factor where the two limits become different:

In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk.

The central limit theorem and the law of the iterated logarithm describe important aspects of the behavior of simple random walk on .

Feller made fundamental contributions to renewal theory, Tauberian theorems, random walks, diffusion processes, and the law of the iterated logarithm.

An even stronger uniform convergence result for the empirical distribution function is available in the form of an extended type of law of the iterated logarithm.

His thesis was in the area of probability in Banach spaces, and solved a problem related to the law of the iterated logarithm for empirical characteristic functions.

S. Ralescu, [6], The law of the iterated logarithm for the multivariate nearest neighbor density estimators, J. Multivar.

This result, now known as Strassen's invariance principle or as Strassen's law of the iterated logarithm, has been highly cited and led to a 1966 presentation at the International Congress of Mathematicians.

More strongly, I. J. Good suggests that the convergence rate of this limit should be significantly faster than that of a random binary sequence, for which (by the law of the iterated logarithm) .

He became one of the founders of modern probability theory, discovering the law of the iterated logarithm in 1924, achieving important results in the field of limit theorems, giving a definition of a stationary process and laying a foundation for the theory of such processes.

Strassen began his researches as a probabilist; his 1964 paper An Invariance Principle for the Law of the Iterated Logarithm defined a functional form of the law of the iterated logarithm, showing a form of scale invariance in random walks.