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Long-term behaviour of refracted Lévy processes in a half-line
Ramkrishna Jyoti Samanta, Alexander R. Watson
Source abstract
We study the long-term behaviour of refracted Lévy processes within a half-line, with killing on exiting the domain and at state-dependent rate inside it. We identify the decay rate of the killed semigroup together with the associated invariant function and measure, and we obtain convergence at exponential rate to a Yaglom limit. The proofs make use of R-theory and Lyapunov function techniques.
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