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

The Landau Equation for Maxwellian molecules and the Brownian Motion on SO_R(N)

In this paper we prove that the spatially homogeneous Landau equation for Maxwellian molecules can be represented through the product of two elementary processes. The first one is the Brownian motion on the group of rotations. The second one is, conditionally on the first one, a Gaussian process. Using this representation, we establish sharp multi-scale upper and lower bounds for the transition density of the Landau equation, the multi-scale structure depending on the shape of the support of the initial condition.Comment: 3