Some Martingales Associated With Multivariate Bessel Processes
2020
We study Bessel processes on Weyl chambers of types A and B
on
$$\mathbb{R}^N$$
. Using elementary symmetric functions, we present several space-timeharmonic
functions and thus martingales for these processes
$$(X_t)_{t\ge0}$$
which are
independent from one parameter of these processes. As a consequence,
$$p_t(y):= \mathbb{E}(\prod_{i=1}^N (y-X_t^i))$$
can be expressed via classical orthogonal polynomials. Such
formulas on characteristic polynomials admit interpretations in random matrix
theory where they are partially known by Diaconis, Forrester, and Gamburd.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
26
References
3
Citations
NaN
KQI