Risk-Sensitive Probability for Markov Chains

摘要

The probability distribution of a Markov chain is viewed as the information state of an additive optimization problem. This optimization problem is then generalized to a product form whose information state gives rise to a generalized notion of probability distribution for Markov chains. The evolution and the asymptotic behavior of this generalized or 'risk-sensitive' probability distribution is studied in this paper and a conjecture is proposed regarding the asymptotic periodicity of risk-sensitive probability. The relation between a set of simultaneous nonlinear equations and the set of periodic attractors is analyzed.