AISM 50, 433-450
© 1998 ISM
(Received April 15, 1996; revised June 23, 1997)
Abstract. In this paper we characterize the local structure of monotone and regular divergences, which include $f$-divergences as a particular case, by giving their Taylor expansion up to fourth order. We extend a previous result obtained by Cencov, using the invariant properties of Amari's $\alpha$-connections.
Key words and phrases: Differential geometry, divergence, embedding invariance, Markov embedding, \alpha-connection.
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