Rough paths and 1d sde with a time dependent distributional drift. Application to polymers

Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional stochastic differential equations, the drift of which is a distribution, by means of rough paths theory. Existence and uniqueness are established in the weak sense when the drift reads as the derivative of a H{\"o}lder continuous function. Regularity of the drift part is investigated carefully and a related stochastic calculus is also proposed, which makes the structure of the solutions more explicit than within the earlier framework of Dirichlet processes

A forward--backward stochastic algorithm for quasi-linear PDEs

We propose a time-space discretization scheme for quasi-linear parabolic PDEs. The algorithm relies on the theory of fully coupled forward--backward SDEs, which provides an efficient probabilistic representation of this type of equation. The derivated algorithm holds for strong solutions defined on any interval of arbitrary length. As a bypass product, we obtain a discretization procedure for the underlying FBSDE. In particular, our work provides an alternative to the method described in [Douglas, Ma and Protter (1996) Ann. Appl. Probab. 6 940--968] and weakens the regularity assumptions required in this reference.Comment: Published at http://dx.doi.org/10.1214/105051605000000674 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward-backward stochastic differential equations and introduce the new concept of ``auxiliary SDEs.''Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000014

Eliminating social inequality by reinforcing standard language ideology? Language policy for Dutch in Flemish schools

Flanders, the northern, Dutch-speaking part of Belgium, is facing a growing intra- and interlingual diversity. On the intralingual level, Tussentaal ('in-between-language') emerged as a cluster of intermediate varieties between the Flemish dialects and Standard Dutch, gradually becoming the colloquial language. At the same time, Flanders counts a growing number of immigrants and languages. This paper analyses the way Flemish language-in-education policy deals with these (perceived) problems of substandardisation and multilingualism, in order to create equal opportunities for all pupils, regardless of their native language or social background. Both the policy and the measures it proposes are strongly influenced by different, yet intertwined ideologies of standardisation and monolingualism. By propagating Standard Dutch as the only acceptable language (variety) and denying all forms of language diversity, Flemish language-in-education policy not only fails to create equal opportunities, but reinforces ideologies that maintain inequality. Instead, language policy should be open towards language diversity, taking the role of teachers in forming and implementing policies into consideration

Mobilizing Cities towards a Low Carbon Future: Tambourines, Carrots and Sticks

In the transition towards a decarbonized energy system, we need city authorities to lead by example as public actors, to govern the actions of the private urban actors as local policy makers, and to conceive and manage the implementation of an integrated approach as coordinators, which we introduce in this paper as three levels of city smartness. Local governments however have institutional disincentives to act, and if they do act, they are confronted with urban actors that are reluctant to follow. This paper analyzes how city pioneers in Europe have been able to overcome these disincentives thanks to a combination of local circumstances and interventions by higher levels of government. We categorize the state of the art instruments that have been used by higher levels of government into “tambourines”, “carrots”, and “sticks”, and reflect on how the state of the art could be improved.cities; climate change; governance

Information Transmission under Random Emission Constraints

We model the transmission of a message on the complete graph with n vertices and limited resources. The vertices of the graph represent servers that may broadcast the message at random. Each server has a random emission capital that decreases at each emission. Quantities of interest are the number of servers that receive the information before the capital of all the informed servers is exhausted and the exhaustion time. We establish limit theorems (law of large numbers, central limit theorem and large deviation principle), as n tends to infinity, for the proportion of visited vertices before exhaustion and for the total duration. The analysis relies on a construction of the transmission procedure as a dynamical selection of successful nodes in a Galton-Watson tree with respect to the success epochs of the coupon collector problem

Convergence order of upwind type schemes for transport equations with discontinuous coefficients

An analysis of the error of the upwind scheme for transport equation with discontinuous coefficients is provided. We consider here a velocity field that is bounded and one-sided Lipschitz continuous. In this framework, solutions are defined in the sense of measures along the lines of Poupaud and Rascle's work. We study the convergence order of the upwind scheme in the Wasserstein distances. More precisely, we prove that in this setting the convergence order is 1/2. We also show the optimality of this result. In the appendix, we show that this result also applies to other "diffusive" "first order" schemes and to a forward semi-Lagrangian scheme