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Quasistationary distributions for one-dimensional diffusions with killing

Abstract:

We extend some results on the convergence of one-dimensional diffusions killed at the boundary, conditioned on extended survival, to the case of general killing on the interior. We show, under fairly general conditions, that a diffusion conditioned on long survival either runs off to infinity almost surely, or almost surely converges to a quasistationary distribution given by the lowest eigenfunction of the generator. In the absence of internal killing, only a sufficiently strong inward drift...

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Publication status:
Published

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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Journal:
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume:
359
Issue:
3
Pages:
1285-1324
Publication date:
2004-06-03
DOI:
ISSN:
0002-9947
URN:
uuid:e3a190ec-cd38-44e3-9dba-381c3a1afc0e
Source identifiers:
97767
Local pid:
pubs:97767
Language:
English
Keywords:

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