Laplacian and Brownian motion on positive definite matrices, revisited

Hiroyuki Matsumoto and Jun Otani

Statistics & Probability Letters, 2023, vol. 193, issue C

Abstract: We present explicit expression for the Laplace–Beltrami operator on the symmetric space of positive definite matrices by using the Iwasawa decomposition and study the corresponding diffusion process, the Brownian motion. We show that some inductive arguments in the dimensions work.

Keywords: Diffusion process; Brownian motion; Symmetric space; Positive definite matrices; Laplace–Beltrami operator (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2022.109696

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