Work

Characterization of exponential families of lumpable stochastic matrices

Year: 2026

Type: article

Abstract: It is known that the set of lumpable Markov chains over a finite state space, with respect to a fixed lumping function, generally does not form an exponential family of stochastic matrices. In this work, we explore efficiently verifiable necessary and sufficient conditions for families of lumpable transition matrices to form exponential families. To this end, we develop a broadly applicable dimension-based method for determining whether a given family of stochastic matrices forms an exponential family.

Source: Information Geometry

DOI: 10.1007/s41884-026-00194-7

Authors: Shun Watanabe, Geoffrey Wolfer

Institution: Tokyo University of Agriculture and Technology

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Japan Society for the Promotion of Science, Japan Science and Technology Agency