11 citations · 38 across the 25 of their papers we have counts for
5 papers · 1 filter
Homogenization of nonlocal equations in randomly evolving media. Diffusion approximation
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
The paper deals with homogenization and higher order approximations of solutions to nonlocal evolution equations of convolution type whose coefficients are periodic in the spatial…
Continuity problem for singular BSDE with random terminal time
Alexandre Popier, Sharoy Samuel, Ali Sezer
We study a class of nonlinear BSDEs with a superlinear driver process f adapted to a filtration F and over a random time interval [[0, S]] where S is a stopping time of F. The term…
Asymptotic decomposition of solutions to parabolic equations with a random microstructure
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
We consider a Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationar…
On the fundamental solution of heat and stochastic heat equations
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
We consider the generic divergence form second order parabolic equation with coefficients that are regular in the spatial variables and just measurable in time. We show that the sp…
Integro-partial differential equations with singular terminal condition
Alexandre Popier
In this paper, we show that the minimal solution of a backward stochastic differential equation gives a probabilistic representation of the minimal viscosity solution of an integro…