Uniform convergence of conditional distributions for absorbed one-dimensional diffusions
| Autor: | Denis Villemonais, Nicolas Champagnat |
|---|---|
| Přispěvatelé: | TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Spectral theory Uniform convergence Primary: 60J60 60J70 37A25 60B10 60F99 Secondary: 60G44 60J75 01 natural sciences one-dimensional diffusions 010104 statistics & probability Position (vector) FOS: Mathematics Uniform boundedness Applied mathematics strict local martingales 0101 mathematics Brownian motion Mathematics one dimensional processes with jumps Applied Mathematics MSC Primary: 60J60 60J70 37A25 60B10 60F99. Secondary: 60G44 60J75 010102 general mathematics Probability (math.PR) Conditional probability distribution quasi-stationary distribution [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Distribution (mathematics) uniform exponential mixing property Q-process Local martingale Mathematics - Probability absorbed process |
| Zdroj: | Advances in Applied Probability Advances in Applied Probability, Applied Probability Trust, 2018, 50 (1), pp.178-203. ⟨10.1017/apr.2018.9⟩ Advances in Applied Probability, 2018, 50 (1), pp.178-203. ⟨10.1017/apr.2018.9⟩ |
| ISSN: | 0001-8678 |
| DOI: | 10.1017/apr.2018.9⟩ |
| Popis: | This article studies the quasi-stationary behaviour 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. 35 pages |
| Databáze: | OpenAIRE |
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