ASYMPTOTIC PROPERTIES OF A MEAN-FIELD MODEL WITH A CONTINUOUS-STATE-DEPENDENT SWITCHING PROCESS

作者：Xi Fubao^*; Yin G

来源：Journal of Applied Probability, 2009, 46(1): 221-243.

DOI：10.1239/jap/1238592126

• Mean-field model
• continuous-state-dependent switching
• Markovian switching
• Feller continuity
• strong Feller continuity
• exponential ergodicity
• strong ergodicity

This work is concerned with a class of mean-field models given by a switching diffusion with a continuous-state-dependent switching process. Focusing on asymptotic properties, the regularity or nonexplosiveness, Feller continuity, and strong Feller continuity are established by means of introducing certain auxiliary processes and by making use of the truncations. Based on these results, exponential ergodicity is obtained under the Foster-Lyapunov drift conditions. By virtue of the coupling methods, the strong ergodicity or uniform ergodicity in the sense of convergence in the variation norm is established for the mean-field model with a Markovian switching process. Besides this, several examples are presented for demonstration and illustration.

• 出版日期2009-3
• 单位北京理工大学