Lyapunov criteria for the Feller-Dynkin property of martingale problems. (English) Zbl 1434.60192
Summary: We give necessary and sufficient criteria for the Feller-Dynkin property of solutions to martingale problems in terms of Lyapunov functions. Moreover, we derive a Khasminskii-type integral test for the Feller-Dynkin property of multidimensional diffusions with random switching. For one dimensional switching diffusions with state-independent switching, we provide an integral-test for the Feller-Dynkin property.
MSC:
| 60J25 | Continuous-time Markov processes on general state spaces |
| 60G44 | Martingales with continuous parameter |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
Feller-Dynkin process; \( C_b\)-Feller process; martingale problem; Lyapunov function; switching diffusionsReferences:
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