马尔可夫链的退相干

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE

Finance and Stochastics Pub Date : 2022-02-16 DOI:10.1080/17442508.2022.2124871

F. Fidaleo, E. Vincenzi

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引用次数: 1

摘要

已知在Effros和m -d引入的正则新积下，由任意随机矩阵的外围谱的特征向量所生成的子空间具有(有限维阿贝尔)代数的正则结构。崔。证明了这种随机矩阵作用于该子空间的约束确实是一个-自同构。然后建立了以下新的退相干结果:任何马尔可夫链在将持久部分与瞬态部分分离后编码一个保守动力系统。这一结果对一类相关系统的一般退相干问题给出了部分的解答。

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Decoherence for Markov chains

It is known that the subspace generated by the eigenvectors pertaining to the peripheral spectrum of any stochastic matrix is canonically equipped with a structure of a (finite-dimensional abelian) -algebra under a canonical new product introduced by E.G. Effros and M.-D. Choi. We prove that the restriction of the action of such a stochastic matrix to this subspace is indeed a -automorphism. The following new decoherence result is then established: any Markov chain encodes a conservative -dynamical system, after isolation of the persistent part from the transient one. This result gives a partial answer to the general and currently unsolved decoherence problem for a relevant class of systems.

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来源期刊

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.