Étienne Pardoux

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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 study the bijection between binary Galton–Watson trees in continuous time and their exploration process, both in the subcritical and in the supercritical cases. We then take the limit over renormalized quantities, as the size of the population tends to ∞. We thus deduce Delmas' generalization of the second Ray–Knight theorem.
In this paper a semilinear elliptic PDE with rapidly oscillating coefficients is homoge-nized. The novetly of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of R d. Our fully probabilistic method is based on the connection between PDEs and BSDEs with random terminal time and the(More)
Consider the standard, one dimensional, nonlinear filtering problem for diffusion processes observed in small additive white noise: dX t = b(X t)dt + dB t , dY ε t = γ(X t)dt + εdV t , where B · , V · are standard independent Brownian motions. Denote by q ε 1 (·) the density of the law of Ξ 1 conditioned on σ(Y ε t : 0 ≤ t ≤ 1). We provide " quenched "(More)
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