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

Pei-Sen Li; Xiangqi Zheng; Xiaowen Zhou

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arXiv · 2606.24821

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

Pei-Sen Li·Xiangqi Zheng·Xiaowen Zhou

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Abstract

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.

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Pei-Sen Li, Xiangqi Zheng, Xiaowen Zhou. 2026-06-23. A Pathwise Approach to the Strong Feller Property and Irreducibility of Nonlinear Branching Processes. https://arxiv.org/abs/2606.24821

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