Brownian Motion: The LIL and Some Fine-Scale Properties
In this chapter, we analyze the growth of the Brownian paths \(t\mapsto B_t\) as \(t\rightarrow \infty \).
We study regularity properties of a positive measure in the euclidean space in terms of two square functions which are the multiplicative analogues of the usual martingale square function and of the Lusin area function of a harmonic function. The size of ...