arXiv subjects

Xiangqi Zheng

Publications and source records attributed to Xiangqi Zheng.

4 recordsLinked to original sources

arXiv2026

A Pathwise Approach to the Strong Feller Property and Irreducibility of Nonlinear Branching Processes

We study the strong Feller property and irreducibility for continuous-state nonlinear branching processes defined as solutions to stochastic differential equations with jumps. Due to boundary degeneracy and discontinuous jump coefficients, classical methods do not apply. We develop a pathwise approach combining state-dependent time change, truncated auxiliary processes, and localized coupling to establish these two properties. As applications, we obtain exponential convergence to a unique quasi-stationary distribution in the absorbing case, and uniform exponential ergodicity in the non-absorbing case. This pathwise approach is flexible and can be adapted to a broader class of jump-diffusions without relying on specific coefficient structures.

math.PR↗

arXiv2026

Yaglom limits of continuous-state branching processes in Brownian random environment

In this paper, we investigate the asymptotic behavior of continuous-state branching processes in a Brownian random environment (CBBRE) conditioned on non-extinction. For the subcritical case, we prove the existence of the Yaglom limit and derive an explicit representation of its Laplace transform using Kummer confluent hypergeometric functions. Notably, we demonstrate that the Yaglom limit is strictly independent of the initial state of the process across all three subcritical regimes: weakly, intermediately, and strongly subcritical.

math.PR↗

arXiv2022

Moment properties for two-type continuous-state branching processes in random environments

We first derive the recurisions for integer moments of two-type continuous-state branching processes in Lévy random environments. Result shows that the $n$th moment of the process is a polynomial of the initial value of the process with at most $n$ degree. Under some natural condition, the criteria for the existence of $f$-moment of the process are also proved.

math.PR↗

arXiv2022

Wasserstein-type distances of two-type continuous-state branching processes in Lévy random environments

Under natural conditions, we proved the exponential ergodicity in Wasserstein distance of two-type continuous-state branching processes in Lévy random environments with immigration. Furthermore, we expressed accurately the parameters of the exponent. The coupling method and the conditioned branching property play an important role in the approach. Using the tool of superprocesses, the ergodicity in total variance distance is also proved.

math.PR↗