PreprintCC BY-SA 4.0arXiv
Long-term behaviour of refracted Lévy processes in a half-line
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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BibTeX
@misc{samanta2026longterm,
title = {{Long-term behaviour of refracted Lévy processes in a half-line}},
author = {Ramkrishna Jyoti Samanta and Alexander R. Watson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29326},
eprint = {2609.29326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29326},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Long-term behaviour of refracted Lévy processes in a half-line
AU - Ramkrishna Jyoti Samanta
AU - Alexander R. Watson
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29326
UR - https://arxiv.org/abs/2609.29326
AB - 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.
ER -