Numerical simulation of BSDEs with drivers of quadratic growth

This article deals with the numerical resolution of Markovian backward stochastic differential equations (BSDEs) with drivers of quadratic growth with respect to $z$ and bounded terminal conditions. We first show some bound estimates on the process $Z$ and we specify the Zhang's path regularity theorem. Then we give a new time discretization scheme with a non uniform time net for such BSDEs and we obtain an explicit convergence rate for this scheme

A stability approach for solving multidimensional quadratic BSDEs

We establish an existence and uniqueness result for a class of multidimensional quadratic backward stochastic differential equations (BSDE). This class is characterized by constraints on some uniform a priori estimate on solutions of a sequence of approximated BSDEs. We also present effective examples of applications. Our approach relies on the strategy developed by Briand and Elie in [Stochastic Process. Appl. 123 2921--2939] concerning scalar quadratic BSDEs.Comment: This update contains corrections for Propositions 5.1 and 5.

A note on the existence of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition

In [Stochastc Process. Appl., 122(9):3173-3208], the author proved the existence and the uniqueness of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition when the generator and the terminal condition are locally Lipschitz. In this paper, we prove that the existence result remains true for these BSDEs when the regularity assumptions on the terminal condition is weakened

Numerical stability analysis of the Euler scheme for BSDEs

In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in the one-dimensional and multidimensional case to guarantee the numerical stability. We then perform a classical Von Neumann stability analysis in the case of a linear driver $f$ and exhibit necessary conditions to get stability in this case. Finally, we illustrate our results with numerical applications

La Família i el mas en les estratègies patrimonials al Vilassar baixmedieval

L'evolució d'un mas i la família que hi habita és accessible mitjançant l'estudi de la base antroponímica i toponímica del mas. L'anàlisi d'aquesta interdependència reflecteix l'existència de fases d'estabilitat, de creixement i d'involució. Dins d'aquesta darrera fase, destaca l'aparició de masos deshabitats, rònecs i derruïts, així com l'aglevament d'aquests masos per pagesos vilassarencs.The tenant family and the farmhouse heritage strategies in the late medieval Vilassar. The evolution of the mas (farmhouse) and the tenant family is approachable by studying its family and place names. The analysis of this interdependence reveals the existence of phases of stability, growth and recession. Within this last phase it has to be highlighted the appearance of vacant, deserted and demolished farms, as well as their acquisition by farmers from Vilassar

El Baix Maresme a l'època baixmedieval

Aquest article és un resum de la nostra tesi doctoral, que ha tingut com a objecte d'estudi la pagesia baixmaresmenca durant el període 1348-1486. La investigació s'ha realitzat a partir de l'anàlisi de tres àmbits d'actuació de la vida quotidiana pagesa baixmedieval: la terra, la família i la mort. D'aquesta manera, es copsen relacions de diversa tipologia mitjançant documentació, fonamentalment generada per aquesta classe social. Per aquesta raó, la nostra investigació complementa recerques anteriors, que analitzen l'àmbit d'actuació senyorial, i contribueix a generar un major coneixement de la Catalunya Vella baixmedieval.This article is a summary of our thesis, whose objective was the study of the peasantry in south Maresme from 1348 to 1486. The research was carried out starting from the analysis of three main aspects in the everyday life of the country people: land, family and death. We see different types of relationships through several documents originated from that social class. For this reason, our work supplements previous researches and contributes to a major knowledge of the Low-Medieval Old Catalonia

Wall effects on the transportation of a cylindrical particle in power-law fluids

The present work deals with the numerical calculation of the Stokes-type drag undergone by a cylindrical particle perpendicularly to its axis in a power-law fluid. In unbounded medium, as all data are not available yet, we provide a numerical solution for the pseudoplastic fluid. Indeed, the Stokes-type solution exists because the Stokes’ paradox does not take place anymore. We show a high sensitivity of the solution to the confinement, and the appearance of the inertia in the proximity of the Newtonian case, where the Stokes’ paradox takes place. For unbounded medium, avoiding these traps, we show that the drag is zero for Newtonian and dilatant fluids. But in the bounded one, the Stokes-type regime is recovered for Newtonian and dilatant fluids. We give also a physical explanation of this effect which is due to the reduction of the hydrodynamic screen length, for pseudoplastic fluids. Once the solution of the unbounded medium has been obtained, we give a solution for the confined medium numerically and asymptotically. We also highlight the consequence of the confinement and the backflow on the settling velocity of a fiber perpendicularly to its axis in a slit. Using the dynamic mesh technique, we give the actual transportation velocity in a power-law “Poiseuille flow”, versus the confinement parameter and the fluidity index, induced by the hydrodynamic interactions

On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions

International audienceIn a previous work, P. Briand and Y. Hu proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved by P. Briand and Y. Hu