7 papers
Parameter Estimation of the Stochastic Allen--Cahn Equation via variations
Simon Chony Acosta, Christian Olivera, Ciprian Tudor
This paper addresses statistical inference for stochastic partial differential equations. We study the stochastic Allen-Cahn equation driven by space-time white noise and analyze i…
An Eulerian-Lagrangian Formulation of the Compressible Euler Equations with Vacuum
Wladimir Neves, Christian Olivera
In this paper, we present a novel Eulerian-Lagrangian formulation for the compressible isentropic Euler equations with vaccum. Using the developed Lagrangian flow map formulation,…
Pathwise quantitative particle approximation of nonlinear stochastic Fokker-Planck equations via relative entropy
Christian Olivera, Alexandre B. de Souza
We derive non-linear stochastic Fokker-Planck equation from stochastic systems particles with individual and environmental noise via relative entropy method, with pathwise quantita…
On local well-posedness of the stochastic incompressible density-dependent Euler equations
Claudia Espitia, David A. C. Mollinedo, Christian Olivera
In this paper we study the stochastic inhomogeneous incompressible Euler equations in the whole space $\RR^3$. We prove the existence and pathwise uniqueness of local solutions wit…
Convergence Rate for Moderate Interaction particles and Application to Mean Field Games
Josué Knorst, Christian Olivera, Alexandre B. de Souza
We study two interacting particle systems, both modeled as a system of stochastic differential equations driven by Brownian motions with singular kernels and moderate interacti…
Microscopic derivation of non-local models with anomalous diffusions from stochastic particle systems
Christian Olivera, Marielle Simon
This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local s…