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A matrix Bougerol identity and the Hua-Pickrell measures. (English) Zbl 1398.60010

Summary: 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.

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60B20 Random matrices (probabilistic aspects)
60J60 Diffusion processes
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References:

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