Uniform convergence of conditional distributions for absorbed one-dimensional diffusions
Uniform convergence of conditional distributions for absorbed one-dimensional diffusions
复制标题
吸收一维扩散的条件分布的均匀收敛
DOI：
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发表时间：
2015
影响因子：
1.2
通讯作者：
D. Villemonais
中科院分区：
文献类型：
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作者：
Nicolas Champagnat;D. Villemonais
本文研究了一维吸收扩散的准定态行为。我们得到了指数收敛到一个唯一的拟平稳分布的必要和充分条件的总变差，一致关于初始分布。一个重要的工具是一维严格的局部鞅扩散从无穷远下降。我们证明，在温和的假设下，他们的期望在任何积极的时间是一致有界的初始位置。我们提供了几个例子和扩展，包括粘性布朗运动和一些一维跳跃过程。
Abstract In this paper we study the quasi-stationary behavior of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation, uniformly with respect to the initial distribution. An important tool is provided by one-dimensional strict local martingale diffusions coming down from infinity. We prove, under mild assumptions, that their expectation at any positive time is uniformly bounded with respect to the initial position. We provide several examples and extensions, including the sticky Brownian motion and some one-dimensional processes with jumps.