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

Abstract

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.