On the notion(s) of duality for Markov processes
On the notion(s) of duality for Markov processes
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DOI：
10.1214/12-ps206
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发表时间：
2014-01-01
影响因子：
1.6
通讯作者：
Kurt, Noemi
中科院分区：
文献类型：
--
作者：
Jansen, Sabine;Kurt, Noemi
我们提供了一个关于函数的马尔可夫过程对偶性概念的系统研究。我们讨论了在马尔可夫过程理论和势理论中所研究的关于测度的这一概念与对偶的关系，并给出了包含存在性和唯一性准则的泛函解析结果和对偶半群谱的比较。解析框架建立在对偶、凸几何和希尔伯特空间的概念之上。此外，我们形式化了路径对偶的概念，因为它出现在群体遗传学和相互作用粒子系统。我们讨论了对偶与重标度、随机单调性、缠结、对称性和量子多体理论的关系，回顾了已知的结果并建立了一些新的联系。
We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory and give functional analytic results including existence and uniqueness criteria and a comparison of the spectra of dual semi-groups. The analytic framework builds on the notion of dual pairs, convex geometry, and Hilbert spaces. In addition, we formalize the notion of pathwise duality as it appears in population genetics and interacting particle systems. We discuss the relation of duality with rescalings, stochastic monotonicity, intertwining, symmetries, and quantum many-body theory, reviewing known results and establishing some new connections.