A Discrete Multivariate Mean Value Theorem with Applications

AMS classifications: 47H10; 54H25; 55M20; 90C33; 91B50Discrete set;mean value theorem;fixed point;algorithm;equilibrium;complementarity

A Discrete Multivariate Mean Value Theorem with Applications

AMS classifications: 47H10; 54H25; 55M20; 90C33; 91B50

Bias in Estimating Multivariate and Univariate Diffusions

Published in Journal of Econometrics, 2011, https://doi.org/10.1016/j.jeconom.2010.12.006</p

Density operators that extremize Tsallis entropy and thermal stability effects

Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PD's as "weights" leads to density operators of a rather general character. The present study allows one to vividly exhibit the effects of non-extensivity. Varying Tsallis' non-extensivity index $q$ one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy.Comment: 22 page