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Two Theorems on Hunt's Hypothesis (H) for Markov Processes | | Ze-Chun Hu
; Wei Sun
; Li-Fei Wang
; | | Date: |
28 Feb 2019 | | Abstract: | We investigate the invariance of Hunt’s hypothesis (H) for Markov processes
under two classes of transformations, which are change of measure and
subordination. Our first theorem shows that for two standard processes $(X_t)$
and $(Y_t)$, if $(X_t)$ satisfies (H) and $(Y_t)$ is locally absolutely
continuous with respect to $(X_t)$, then $(Y_t)$ satisfies (H). Our second
theorem shows that a standard process $(X_t)$ satisfies (H) if and only if
$(X_{ au_t})$ satisfies (H) for some (and hence any) subordinator $( au_t)$
which is independent of $(X_t)$ and has a positive drift coefficient.
Applications of the two theorems are given. | | Source: | arXiv, 1903.0050 | | Services: | Forum | Review | PDF | Favorites | |
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