Bishop parameter $$\chi $$ from static equilibrium

Chi-square Tests for Parameter Stability

Static Equilibrium under Uncertainty and Incomplete Markets

1.1. The first model of general economic equilibrium was presented by Walras [15] more than hundred years ago. As the model became generally known, it must have been clçar that it was desirable to generalize it, and take uncertainty into account. The most visible markets at the end of the last century were probably the stock exchanges, where uncertainty obviously played an important part. Insur...

Large Parameter Behavior of Equilibrium Measures

We study the equilibrium measure for a logarithmic potential in the presence of an external field V∗(ξ) + t p(ξ), where t is a parameter, V∗(ξ) is a smooth function and p(ξ) a monic polynomial. When p(ξ) is of an odd degree, the equilibrium measure is shown to be supported on a single interval as |t| is sufficiently large. When p(ξ) is of an even degree, the equilibrium measure is supported on ...

A Bishop surface with a vanishing Bishop invariant

We derive a complete set of invariants for a formal Bishop surface near a point of complex tangent with a vanishing Bishop invariant under the action of formal transformations. We prove that the modular space of Bishop surfaces with a vanishing Bishop invariant and with a fixed Moser invariant s < ∞ is of infinite dimension. We also prove that the equivalence class of the germ of a generic real...

The Mergelyan-Bishop Theorem

We define the differential operator ∂ ∂z on infinitely differentiable functions (also called smooth or C∞ functions) on some open set in C by ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ). A quick calculation shows that ∂ ∂z obeys the product rule. Recall that a function f is holomorphic if and only if ∂ ∂z (f) = 0. A function is biholomorphic, or an analytic isomorphism, if it is holomorphic and has holomorphi...