Invariant metric under deformed Markov embeddings with overlapped supports

Hiroshi Matsuzoe; Asuka Takatsu

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arXiv · 1910.12226

Invariant metric under deformed Markov embeddings with overlapped supports

Hiroshi Matsuzoe·Asuka Takatsu

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Abstract

Due to \v{C}encov'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 $n\in \mathbb{N}$ under Markov embeddings. We deform Markov embeddings keeping sufficiency, and prove existence and uniqueness of invariant families under the embeddings.

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BibTeX RIS

Hiroshi Matsuzoe, Asuka Takatsu. 2019-10-27. Invariant metric under deformed Markov embeddings with overlapped supports. https://arxiv.org/abs/1910.12226

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