Summary
LetG=(G(t),t≧0) be the process of last passage times at some fixed point of a Markov process. The Dynkin-Lamperti theorem provides a necessary and sufficient condition forG(t)/t to converge in law ast→∞ to some non-degenerate limit (which is then a generalized arcsine law). Under this condition, we give a simple integral test that characterizes the lower-functions ofG. We obtain a similar result forA +=(A + (t),t≧0), the time spent in [0, ∞) by a real-valued diffusion process, in connection with Watanabe's recent extension of Lévy's second arcsine law.
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Bertoin, J. Sample path behaviour in connection with generalized arcsine laws. Probab. Th. Rel. Fields 103, 317–327 (1995). https://doi.org/10.1007/BF01195477
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DOI: https://doi.org/10.1007/BF01195477
Mathematics Subject Classification
- 60G17
- 60J25