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Quasistationary distributions for one-dimensional diffusions with killing
2006
Transactions of the American Mathematical Society
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
doi:10.1090/s0002-9947-06-03980-8
fatcat:gfu3aanvorarvn2yek5nxg3yzq