Тип публикации: статья из журнала
Год издания: 2010
Идентификатор DOI: 10.3390/e12051145
Ключевые слова: Markov process, Lyapunov function, entropy functionals, attainable region, MaxEnt, inference
Аннотация: The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independПоказать полностьюent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally "most random" distributions.
Журнал: ENTROPY
Выпуск журнала: Vol. 12, Is. 5
Номера страниц: 1145-1193
ISSN журнала: 10994300
Место издания: BASEL
Издатель: MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI