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- Etienne Pardoux
- 2010

A new type of stochastic differential equation, called the backward stochastic differentil equation (BSDE), where the value of the solution is prescribed at the final (rather than the initial) point of the time interval, but the solution is nevertheless required to be at each time a function of the past of the underlying Brownian motion, has been introduced… (More)

A new kind of backward stochastic differential equations (in short BSDE), where the solution is a pair of processes adapted to the past of the driving Brownian motion, has been introduced by the authors in [63. It was then shown in a series of papers by the second and both authors (see [8, 7, 9, 103), that this kind of backward SDEs gives a probabilistic… (More)

- Etienne Pardoux
- 1996

The aim of this set of lectures is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semi– linear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs have appeared long time ago, both as the equations for the… (More)

We study a new class of backward stochastic dierential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial dierential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic… (More)

- E. PARDOUX
- 2005

We study the Poisson equation Lu+ f = 0 in R, where L is the infinitesimal generator of a diffusion process. In this paper, we allow the second-order part of the generator L to be degenerate, provided a local condition of Doeblin type is satisfied, so that, if we also assume a condition on the drift which implies recurrence, the diffusion process is… (More)

Let L be a second-order partial differential operator in R e. Let R e be the finite union of disjoint polyhedra. Suppose that the diffusion matrix is everywhere non singular and constant on each polyhedron, and that the drift coefficient is bounded and measurable. We show that the martingale problem associated with L is well-posed.

- E. PARDOUX
- 1986

It is shown that if a diffusion process, {Xt: 0 < t < 1}, on Rd satisfies dXt = b(t, Xt) dt + a(t, Xt) dwt then the reversed process, {Xt: 0 < t < 1} where Xt = Xl t , is again a diffusion with drift b and diffusion coefficient a, provided some mild conditions on b, a, and p(, the density of the law of X(, hold. Moreover b and a are identified. 1.… (More)

- C Donati-Martin, E Pardoux
- 1991

We study reflected solutions of a nonlinear heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by space-time white noise. The nonlinearity appears both in the drift and in the diffusion coefficient. Roughly speaking, at any point (t, x) where the solution u(t, x) is strictly positive it obeys the equation, and at a point… (More)

- Bogdan Iftimie, Étienne Pardoux, Andrey Piatnitski, A. Piatnitski
- 2006

This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It… (More)

We give a new proof for a Ray-Knight representation of Feller’s branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion H with a drift that is affine linear in the local time accumulated by H at its current level. In [5], such a representation was obtained by an approximation through Harris paths that code the… (More)