Adapted solution of a backward stochastic differential equation
- É. Pardoux, S. Peng
- Mathematics
- 3 January 1990
Backward stochastic differential equations and quasilinear parabolic partial differential equations
- É. Pardoux, S. Peng
- Mathematics
- 1992
Backward doubly stochastic differential equations and systems of quasilinear SPDEs
- É. Pardoux, S. Peng
- Mathematics
- 1 June 1994
SummaryWe introduce a new class of backward stochastic differential equations, which allows us to produce a probabilistic representation of certain quasilinear stochastic partial differential…
Reflected solutions of backward SDE's, and related obstacle problems for PDE's
- N. Karoui, C. Kapoudjian, É. Pardoux, S. Peng, M. Quenez
- Mathematics
- 1 April 1997
We study reflected solutions of one-dimensional backward stochastic differential equations. The “reflection” keeps the solution above a given stochastic process. We prove uniqueness and existence…
Backward stochastic differential equations and integral-partial differential equations
- G. Barles, R. Buckdahn, É. Pardoux
- Mathematics
- 1 February 1997
We consider a backward stochastic differential equation, whose data (the final condition and the coefficient) are given functions of a jump-diffusion process. We prove that under mild conditions the…
Stochastic calculus with anticipating integrands
- D. Nualart, É. Pardoux
- Mathematics
- 1 August 1988
SummaryWe study the stochastic integral defined by Skorohod in [24] of a possibly anticipating integrand, as a function of its upper limit, and establish an extended Itô formula. We also introduce an…
BSDEs, weak convergence and homogenization of semilinear PDEs
- É. Pardoux
- Mathematics
- 1999
In these lectures, we present the theory of backward stochastic differential equations, and its connection with solutions of semilinear second order partial differential equations of parabolic and…
On the poisson equation and diffusion approximation 3
- É. Pardoux, A. Veretennikov
- Mathematics
- 1 July 2001
Three different results are established which turn out to be closely connected so that the first one implies the second one which in turn implies the third one. The first one states the smoothness of…
BACKWARDS SDE WITH RANDOM TERMINAL TIME AND APPLICATIONS TO SEMILINEAR ELLIPTIC PDE
- R. Darling, É. Pardoux
- Mathematics
- 1 July 1997
Suppose {F t } is the filtration induced by a Wiener process W in R d , τ is a finite {F t } stopping time (terminal time), ξ is an F τ -measurable random variable in R k (terminal value) and f(.,…
White noise driven quasilinear SPDEs with reflection
- D. Nualart, É. Pardoux
- Mathematics
- 1 March 1992
SummaryWe study reflected solutions of the heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise. Roughly speaking, at any…
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