1,820 research outputs found
Smallness of a commodity and partial equilibrium analysis
Partial equilibrium analysis has a conceptual dilemma that its object should be negligibly small in order to be free from income effect but then the consumer does not care for it and the notion of willingness to pay for it does not make sense. In the setting of a continuum of commodities, we propose a limiting procedure which transforms the general many-commodity framework into a partial single-commodity framework. In the limit, willingness to pay for a commodity is established as a density notion and it is shown to be free from income effect. This pins down an exact relationship between general equilibrium analysis and partial equilibrium analysis
Convergence of values in optimal stopping
Under the hypothesis of convergence in probability of a sequence of
c\`adl\`ag processes to a c\`adl\`ag process , we are interested
in the convergence of corresponding values in optimal stopping. We give results
under hypothesis of inclusion of filtrations or convergence of filtrations
Optimal transportation with traffic congestion and Wardrop equilibria
In the classical Monge-Kantorovich problem, the transportation cost only
depends on the amount of mass sent from sources to destinations and not on the
paths followed by this mass. Thus, it does not allow for congestion effects.
Using the notion of traffic intensity, we propose a variant taking into account
congestion. This leads to an optimization problem posed on a set of probability
measures on a suitable paths space. We establish existence of minimizers and
give a characterization. As an application, we obtain existence and variational
characterization of equilibria of Wardrop type in a continuous space setting
Convergence groups from subgroups
We give sufficient conditions for a group of homeomorphisms of a Peano
continuum X without cut-points to be a convergence group. The condition is that
there is a collection of convergence subgroups whose limit sets `cut up' X in
the correct fashion. This is closely related to the result in [E Swenson, Axial
pairs and convergence groups on S^1, Topology 39 (2000) 229-237].Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol6/paper22.abs.htm
Polyhedral computational geometry for averaging metric phylogenetic trees
This paper investigates the computational geometry relevant to calculations
of the Frechet mean and variance for probability distributions on the
phylogenetic tree space of Billera, Holmes and Vogtmann, using the theory of
probability measures on spaces of nonpositive curvature developed by Sturm. We
show that the combinatorics of geodesics with a specified fixed endpoint in
tree space are determined by the location of the varying endpoint in a certain
polyhedral subdivision of tree space. The variance function associated to a
finite subset of tree space has a fixed algebraic formula within
each cell of the corresponding subdivision, and is continuously differentiable
in the interior of each orthant of tree space. We use this subdivision to
establish two iterative methods for producing sequences that converge to the
Frechet mean: one based on Sturm's Law of Large Numbers, and another based on
descent algorithms for finding optima of smooth functions on convex polyhedra.
We present properties and biological applications of Frechet means and extend
our main results to more general globally nonpositively curved spaces composed
of Euclidean orthants.Comment: 43 pages, 6 figures; v2: fixed typos, shortened Sections 1 and 5,
added counter example for polyhedrality of vistal subdivision in general
CAT(0) cubical complexes; v1: 43 pages, 5 figure
- …