The tail behavior of Cox–Ingersoll–Ross processes with state-dependent switching

Abstract

As a continuation of the study by Hou and Shao [Sci. China Math., 63 (2020), pp. 1169-1180], this work makes three key advances in studying state-dependent switching Cox–Ingersoll–Ross processes. First, we establish tail behavior results for stationary distributions across both finite and infinite regimes-a significant extension beyond their framework. Second, through novel auxiliary Markov chains, we explicitly construct a comparison theorem specifically adapted for state-dependent switching diffusions. Third, we derive sufficient recurrence conditions for infinite-regime cases. Our approach provides rigorous control of state-dependent switching component processes with Markov chains and remains applicable to broader classes of state-dependent switching diffusion processes.