期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2017
卷号：XIV
页码：177-199
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：This article studies the quasi-stationary behavior of absorbed onedimensionaldiffusion processes with killing on [0,∞). We obtain criteria for theexponential convergence to a unique quasi-stationary distribution in total variation,uniformly with respect to the initial distribution. Our approach is based onprobabilistic and coupling methods, contrary to the classical approach based onspectral theory results. Our general criteria apply in the case where ∞ is entranceand 0 either regular or exit, and are proved to be satisfied under several explicitassumptions expressed only in terms of the speed and killing measures. We alsoobtain exponential ergodicity results on the Q-process. We provide several examplesand extensions, including diffusions with singular speed and killing measures,general models of population dynamics, drifted Brownian motions and some onedimensionalprocesses with jumps.
关键词：diffusions; one-dimensional diffusions with killing; absorbed process;quasi-stationary distribution; Q-process; uniform exponential mixing property; one dimensional;processes with jumps.
