On the maximal correlation of some stochastic processes
Abstract
We study the maximal correlation coefficient $R(X,Y)$ between two stochastic processes $X$ and $Y$. In the case when $(X,Y)$ is a random walk, we find $R(X,Y)$ using the Csáki-Fischer identity and the lower semicontinuity of the map $\text{Law}(X,Y) \to R(X,Y)$. When $(X,Y)$ is a two-dimensional Lévy process, we express $R(X,Y)$ in terms of the Lévy measure of the process and the covariance matrix of the diffusion part of the process. Consequently, for a two-dimensional $α$-stable random vector $(X,Y)$ with $0
Fields of Study & Subjects
Stochastic processes and financial applications
Publication details
- Journal / source
- The Annals of Applied Probability
- Volume
- 36
- Issue
- 3
- Publication date
- 1 June 2026
- Language
- EN