The Experts below are selected from a list of 34599 Experts worldwide ranked by ideXlab platform
Michael Röckner - One of the best experts on this subject based on the ideXlab platform.
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Probabilistic Representation for solutions of an irregular porous media type equation: the degenerate case
Probability Theory and Related Fields, 2011Co-Authors: Viorel Barbu, Michael RöcknerAbstract:We consider a possibly degenerate porous media type equation over all of $${\mathbb R^d}$$ with d = 1, with monotone discontinuous coefficients with linear growth and prove a Probabilistic Representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution.
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Probabilistic Representation for solutions of an irregular porous media type equation
Annals of Probability, 2010Co-Authors: Philippe Blanchard, Michael RöcknerAbstract:We consider a porous media type equation over all of ℝ d , d = 1, with monotone discontinuous coefficient with linear growth, and prove a Probabilistic Representation of its solution in terms of an associated microscopic diffusion. The interest in such singular porous media equations is due to the fact that they can model systems exhibiting the phenomenon of self-organized criticality. One of the main analytic ingredients of the proof is a new result on uniqueness of distributional solutions of a linear PDE on ℝ 1 with not necessarily continuous coefficients.
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{Probabilistic Representation for solutions of an irregular porous media type equation.
2009Co-Authors: Philippe Blanchard, Michael RöcknerAbstract:We consider a porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a Probabilistic Representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. One of the main analytic ingredients of the proof, is a new result on uniqueness of distributional solutions of a linear PDE on $\R^1$ with non-continuous coefficients.
Gautam Iyer - One of the best experts on this subject based on the ideXlab platform.
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a stochastic lagrangian Representation of the three dimensional incompressible navier stokes equations
Communications on Pure and Applied Mathematics, 2008Co-Authors: Peter Constantin, Gautam IyerAbstract:In this paper we derive a Probabilistic Representation of the deterministic three-dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self-contained proof of local existence for the nonlinear stochastic system and can be extended to formulate stochastic Representations of related hydrodynamic-type equations, including viscous Burgers equations and Lagrangian-averaged Navier-Stokes alpha models. © 2007 Wiley Periodicals, Inc.
Stephane Menozzi - One of the best experts on this subject based on the ideXlab platform.
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a forward backward stochastic algorithm for quasi linear pdes
arXiv: Probability, 2006Co-Authors: Francois Delarue, Stephane MenozziAbstract: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.
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a forward backward stochastic algorithm for quasi linear pdes
Annals of Applied Probability, 2006Co-Authors: Francois Delarue, Stephane MenozziAbstract:We propose a time-space discretization scheme for quasi-linear PDEs. The algorithm relies on the theory of fully coupled Forward-Backward SDEs, which provides an efficient Probabilistic Representation of this type of equations. 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.
Philippe Blanchard - One of the best experts on this subject based on the ideXlab platform.
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Probabilistic Representation for solutions of an irregular porous media type equation
Annals of Probability, 2010Co-Authors: Philippe Blanchard, Michael RöcknerAbstract:We consider a porous media type equation over all of ℝ d , d = 1, with monotone discontinuous coefficient with linear growth, and prove a Probabilistic Representation of its solution in terms of an associated microscopic diffusion. The interest in such singular porous media equations is due to the fact that they can model systems exhibiting the phenomenon of self-organized criticality. One of the main analytic ingredients of the proof is a new result on uniqueness of distributional solutions of a linear PDE on ℝ 1 with not necessarily continuous coefficients.
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{Probabilistic Representation for solutions of an irregular porous media type equation.
2009Co-Authors: Philippe Blanchard, Michael RöcknerAbstract:We consider a porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a Probabilistic Representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. One of the main analytic ingredients of the proof, is a new result on uniqueness of distributional solutions of a linear PDE on $\R^1$ with non-continuous coefficients.
Francois Delarue - One of the best experts on this subject based on the ideXlab platform.
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a forward backward stochastic algorithm for quasi linear pdes
arXiv: Probability, 2006Co-Authors: Francois Delarue, Stephane MenozziAbstract: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.
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a forward backward stochastic algorithm for quasi linear pdes
Annals of Applied Probability, 2006Co-Authors: Francois Delarue, Stephane MenozziAbstract:We propose a time-space discretization scheme for quasi-linear PDEs. The algorithm relies on the theory of fully coupled Forward-Backward SDEs, which provides an efficient Probabilistic Representation of this type of equations. 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.
