Invariant Metric Under Deformed Markov Embeddings with Overlapped Supports

Hiroshi Matsuzoe, Asuka Takatsu

Research output: Contribution to journalArticlepeer-review


Due to Čencov’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.

Original languageEnglish
Article number54
JournalResults in Mathematics
Issue number2
Publication statusPublished - 2021 May
Externally publishedYes


  • Fisher metric
  • Information geometry
  • Markov embedding
  • Čencov’s theorem

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics


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