Classical bi-Poisson process: an invertible quadratic harness

The bi-Poisson process: a quadratic harness

This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam--Chihara polynomials and a relation between these polynomials for different values of parameters.

泊松过程函数的可逆性及其应用

Invertibility of functionals of the Poisson process and applications

研究泊松空间上随机时间变换的可逆性条件，提出Hawkes过程的新构造方法，并建立熵的变分表示。