Lyapunov Criteria for the Feller-Dynkin Property of Martingale Problems
David Criens
TL;DR
This paper establishes criteria based on Lyapunov functions to determine when solutions to martingale problems possess the Feller-Dynkin property, including integral tests for various classes of diffusions.
Contribution
It introduces necessary and sufficient Lyapunov-based criteria for the Feller-Dynkin property in martingale problems, extending to multidimensional and one-dimensional switching diffusions.
Findings
Lyapunov criteria characterize the Feller-Dynkin property.
Integral tests are derived for multidimensional diffusions with switching.
Specific criteria are provided for one-dimensional switching diffusions.
Abstract
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.
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