20,427 research outputs found
Finitely additive beliefs and universal type spaces
The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14
(1967/68) 159--182, 320--334, 486--502] are the prevalent models used to
describe interactive uncertainty. In this paper we examine the existence of a
universal type space when beliefs are described by finitely additive
probability measures. We find that in the category of all type spaces that
satisfy certain measurability conditions (-measurability, for some
fixed regular cardinal ), there is a universal type space (i.e., a
terminal object) to which every type space can be mapped in a unique
beliefs-preserving way. However, by a probabilistic adaption of the elegant
sober-drunk example of Heifetz and Samet [Games Econom. Behav. 22 (1998)
260--273] we show that if all subsets of the spaces are required to be
measurable, then there is no universal type space.Comment: Published at http://dx.doi.org/10.1214/009117905000000576 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Decompositions of Measures on Pseudo Effect Algebras
Recently in \cite{Dvu3} it was shown that if a pseudo effect algebra
satisfies a kind of the Riesz Decomposition Property ((RDP) for short), then
its state space is either empty or a nonempty simplex. This will allow us to
prove a Yosida-Hewitt type and a Lebesgue type decomposition for measures on
pseudo effect algebra with (RDP). The simplex structure of the state space will
entail not only the existence of such a decomposition but also its uniqueness
Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces
We develop a Thermodynamic Formalism for bounded continuous potentials
defined on the sequence space , where is a general
Borel standard space. In particular, we introduce meaningful concepts of
entropy and pressure for shifts acting on and obtain the existence of
equilibrium states as additive probability measures for any bounded continuous
potential. Furthermore, we establish convexity and other structural properties
of the set of equilibrium states, prove a version of the
Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity
of the potential and show that the Yosida-Hewitt decomposition of these
equilibrium states do not have a purely additive part.
We then apply our results to the construction of invariant measures of
time-homogeneous Markov chains taking values on a general Borel standard space
and obtain exponential asymptotic stability for a class of Markov operators. We
also construct conformal measures for an infinite collection of interacting
random paths which are associated to a potential depending on infinitely many
coordinates. Under an additional differentiability hypothesis, we show how this
process is related after a proper scaling limit to a certain infinite
dimensional diffusion.Comment: Accepted for publication in Discrete and Continuous Dynamical
Systems. 23 page
*-Continuous Kleene -Algebras for Energy Problems
Energy problems are important in the formal analysis of embedded or
autonomous systems. Using recent results on star-continuous Kleene
omega-algebras, we show here that energy problems can be solved by algebraic
manipulations on the transition matrix of energy automata. To this end, we
prove general results about certain classes of finitely additive functions on
complete lattices which should be of a more general interest.Comment: In Proceedings FICS 2015, arXiv:1509.0282
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