A matrix Bougerol identity and the Hua-Pickrell measures

Electronic Communications in Probability

Theodoros Assiotis¹ 

关键词: random matrices;    stochastic processes;    integrable probability;   

DOI  :  10.1214/18-ECP107

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We prove a Hermitian matrix version of Bougerol’s identity. Moreover, we construct the Hua-Pickrell measures on Hermitian matrices, as stochastic integrals with respect to a drifting Hermitian Brownian motion and with an integrand involving a conjugation by an independent, matrix analogue of the exponential of a complex Brownian motion with drift.

【 授权许可】

CC BY