We study the absolute continuity of the image measure of the canonical Poisson probability measure under nonlinear shifts. The Radon-Nykodim density function is expressed using a Carleman-Fredholm determinant and a divergence operator. Results are obtained for non-necessarily invertible transformations, under almost-sure differentiability hypothesis.

We introduce a new class of rules for resolving quasilinear social choice problems. These rules extend those of Green [6]. We call such rules multi-utilitarian rules. Each multi-utilitarian rule is associated with a probability measure over the set of weighted utilitarian rules, and is derived as the expectation of this probability. These rules are characterized by the axioms efficiency, transl...

In this paper, new conditions for the stability of V -geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher regularity properties are investigated. As an illustration, an asymptotic expansion of the invariant probability measure for an autoregressive model with i....

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game’s expected payoff fu...

Let f : M → M be a C 1 diffeomorphism of a compact manifold M admitting a dominated splitting T M = E cs ⊕ E cu. We show that if the Lyapunov exponents of f are nonzero and have the same sign along the E cs and E cu directions on a total probability set (a set with probability one with respect to every f-invariant measure), then f is Axiom A. We also show that a f-ergodic measure whose Lyapunov...