@article{7b16971de6c546aa9cf17161ea1badc9,
title = "Invariant Metric Under Deformed Markov Embeddings with Overlapped Supports",
abstract = "Due to {\v C}encov{\textquoteright}s theorem, there exists a unique family of invariant symmetric (0, 2)-tensor fields on the space of positive probability measures on a set of n-points indexed by n∈ N under Markov embeddings. We deform Markov embeddings keeping sufficiency, and prove existence and uniqueness of invariant families under the embeddings.",
keywords = "Fisher metric, Information geometry, Markov embedding, {\v C}encov{\textquoteright}s theorem",
author = "Hiroshi Matsuzoe and Asuka Takatsu",
note = "Funding Information: The both authors express their sincere gratitude to Professor Akio Fujiwara for his valuable comments on sufficient statistics. The authors also would like to thank Professor Hitoshi Furuhata for stimulating discussion. HM was supported in part by JSPS Grant-in-Aid for Scientific Research (KAKENH) 19K03489. AT was supported in part by KAKENHI 19K03494, 19H01786. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.",
year = "2021",
month = may,
doi = "10.1007/s00025-021-01358-w",
language = "English",
volume = "76",
journal = "Results in Mathematics",
issn = "1422-6383",
publisher = "Birkhauser Verlag Basel",
number = "2",
}