Quadratic transportation inequalities for SDEs with measurable drift

Autor: Soufiane Mouchtabih, Ludovic Tangpi, Khaled Bahlali

Publikováno v: Proceedings of the American Mathematical Society. 149:3583-3596

Let X X be the solution of a stochastic differential equation in Euclidean space driven by standard Brownian motion, with measurable drift and Sobolev diffusion coefficient. In our main result we show that when the drift is measurable and the diffusi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::979d760502bdfef54f011612914ea28c
https://doi.org/10.1090/proc/15477

Penalization for a PDE with a nonlinear Neumann boundary condition and measurable coefficients

Autor: Brahim Boufoussi, Khaled Bahlali, Soufiane Mouchtabih

Publikováno v: Stochastics and Dynamics. 22

We consider a system of semilinear partial differential equations (PDEs) with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized PDEs, which converges to our initial problem. Since the coeffi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::dd934286e886b96d8484b2c62f612ff5
https://doi.org/10.1142/s0219493721500532

Averaging for BSDEs with null recurrent fast component. Application to homogenization in a non periodic media

Autor: Abouo Elouaflin, Etienne Pardoux, Khaled Bahlali

Publikováno v: Stochastic Processes and their Applications
Stochastic Processes and their Applications, Elsevier, 2017, 127, pp.1321-1353. ⟨10.1016/j.spa.2016.08.001⟩
Stochastic Processes and their Applications, 2017, 127, pp.1321-1353. ⟨10.1016/j.spa.2016.08.001⟩
Stochastic Processes and their Applications, 2017, ⟨10.1016/j.spa.2016.08.001⟩

We establish an averaging principle for a family of solutions ( X e , Y e ) : = ( X 1 , e , X 2 , e , Y e ) of a system of decoupled forward backward stochastic differential equations (SDE-BSDE for short) with a null recurrent fast component X 1 , e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ef5434433833d711b3db4c69cbf9397
https://doi.org/10.1016/j.spa.2016.08.001

Existence of an optimal control for a coupled FBSDE with a non degenerate diffusion coefficient

Autor: Khaled Bahlali, Brahim Mezerdi, Ahmed Mtiraoui, Omar Kebiri

Publikováno v: Stochastics: An International Journal of Probability and Stochastic Processes
Stochastics: An International Journal of Probability and Stochastic Processes, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2018, 90 (6), pp.861-875. ⟨10.1080/17442508.2018.1427750⟩
Stochastics: An International Journal of Probability and Stochastic Processes, 2018, 90 (6), pp.861-875. ⟨10.1080/17442508.2018.1427750⟩

We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential equation (B

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f5fea5d068dd42416fc09ab724a1718f
https://hal-univ-tln.archives-ouvertes.fr/hal-01824474

Quadratic BSDE with $\mathbb{L}^{2}$-terminal data: Krylov’s estimate, Itô–Krylov’s formula and existence results

Autor: Khaled Bahlali, Youssef Ouknine, M’hamed Eddahbi

Publikováno v: Annals of Probability
Annals of Probability, Institute of Mathematical Statistics, 2017, 45 (4), pp.2377-2397. ⟨10.1214/16-AOP1115⟩
Ann. Probab. 45, no. 4 (2017), 2377-2397

We establish a Krylov-type estimate and an Ito–Krylov change of variable formula for the solutions of one-dimensional quadratic backward stochastic differential equations (QBSDEs) with a measurable generator and an arbitrary terminal datum. This al

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::70f07868ee9d07ce84f1304e32eb512a
https://hal-univ-tln.archives-ouvertes.fr/hal-01824223