2024/11/26 by Chang, Yinshan, Chen, Qinwei · 1 citation
#60G51 #62H20 #62J10 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2411.17109
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 Law(X,Y) → 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<α<2, we express R(X,Y) in terms of α and the spectral measure τ of the α-stable distribution. We also establish analogs and extensions of the Dembo-Kagan-Shepp-Yu inequality and the Madiman-Barron inequality.