A REVERSE ERGODIC THEOREM FOR INHOMOGENEOUS KILLED MARKOV CHAINS AND APPLICATION TO A NEW UNIQUENESS RESULT FOR REFLECTING DIFFUSIONS

• 成果类型: Article
• 署名作者: Costantini, Cristina; Kurtz, Thomas G.
• 署名单位: G d'Annunzio University of Chieti-Pescara; G d'Annunzio University of Chieti-Pescara; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2047
• 发表日期: 2024
• 页码: 3665-3700
• 关键词: brownian-motion; approximation; EXISTENCE; wedge

摘要

Bass and Pardoux ( Probab. Theory Related Fields (1987) 76 557-572) deduce from the Krein-Rutman theorem a reverse ergodic theorem for a sub- probability transition function, which turns out to be a key tool in proving uniqueness of reflecting Brownian motion in cones in Kwon and Williams ( Trans. Amer. Math. Soc (1991) 32 739-780) and Taylor and Williams ( Probab. Theory Related Fields (1993) 96 283-317). By a different approach, we are able to prove an analogous reverse ergodic theorem for a family of in- homogeneous subprobability transition functions. This allows us to prove existence and uniqueness for a semimartingale diffusion process with varying, oblique direction of reflection, in a domain with one singular point that can be approximated, near the singular point, by a smooth cone, under natural, easily verifiable geometric conditions. Along the way we also show that, under our conditions, the parameter alpha of Kwon and Williams (1991) is strictly less than 1, thus partially extending the results of Williams (Z. Z. Warsch. Verw. Gebiete (1985) 69 161-176) to higher dimension.