Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Rough solutions for the periodic Korteweg--de~Vries equation

Abstract: We show how to apply ideas from the theory of rough paths to the analysis of low-regularity solutions to non-linear dispersive equations. Our basic example will be the one dimensional Korteweg– de Vries (KdV) equation on a periodic domain and with initial condition in FL �,p spaces. We discuss convergence of Galerkin approximations, a modified Euler scheme and the presence of a random force of white-noise type in time.

Approximation algorithms and hardness results for labeled connectivity problems

Abstract: Let G = (V, E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function £: E → N. In addition, each label e N to which at least one edge is mapped has a non-negative cost c( ). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of labels I c N such that the edge set {e e E: £(e) e I} forms a connected subgraph spanning all vertices. Similarly, in the minimum label s-t path problem (MinLP) the goal is to identify an s-t path minimizing the combined cost of its labels, where s and t are provided as part of the input. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP. As a secondary objective, we make a concentrated effort to relate the algorithmic methods utilized in approximating these problems to a number of well-known techniques, originally studied in the context of integer covering.

A stochastic target formulation for optimal switching problems in finite horizon

Abstract: We consider a general optimal switching problem for a controlled diffusion and show that its value coincides with the value of a well-suited stochastic target problem associated to a diffusion with jumps. The proof consists in showing that the Hamilton–Jacobi–Bellman equations of both problems are the same and in proving a comparison principle for this equation. This provides a new family of lower bounds for the optimal switching problem, which can be computed by Monte-Carlo methods. This result has also a nice economical interpretation in terms of a firm's valuation.