Some martingales associated with multivariate Jacobi processes and Aomoto's Selberg integral
英文摘要：
We study $β$-Jacobi diffusion processes on alcoves in $\mathbb R^N$, depending on 3 parameters. Using elementary symmetric functions, we present space-time-harmonic functions and martingales for these processes $(X_t)_{t\ge0}$ which are independent from one parameter. This leads to a formula for $\mathbb E(\prod_{i=1}^N (y-X_{t,i}))$ in terms of classical Jacobi polynomials. For $t\to\infty$ this yields a corresponding formula for Jacobi ensembles and thus Aomoto's Selberg integral.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
