Extreme-Value Analysis of Standardized Gaussian Increments

Zakhar Kabluchko

Let $\{X_i,i=1,2,...\}$ be i.i.d. standard gaussian variables. Let $S_n=X_1+...+X_n$ be the sequence of partial sums and $$L_n=\underset{0\le i<j\le n}{\max }\frac{S_j-S_i}{\sqrt{j-i}}.$$…