A REGULARIZED KELLERER THEOREM IN ARBITRARY DIMENSION

• 成果类型: Article
• 署名作者: Pammer, Gudmund; Robinson, Benjamin A.; Schachermayer, Walter
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Klagenfurt; University of Vienna
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2125
• 发表日期: 2025
• 页码: 749-778
• 关键词: mimicking

摘要

We present a multidimensional extension of Kellerer's theorem on the existence of mimicking Markov martingales for peacocks, a term derived from the French for stochastic processes increasing in convex order. For a continuous-time peacock in arbitrary dimension, after Gaussian regularization, we show that there exists a strongly Markovian mimicking martingale It & ocirc; diffusion. A novel compactness result for martingale diffusions is a key tool in our proof. Moreover, we provide counterexamples to show, in dimension d >= 2, that uniqueness may not hold, and that some regularization is necessary to guarantee existence of a mimicking Markov martingale.