| Abstract: |
| By Itos formula the time marginals of a solution to a distribution dependent SDE solve a nonlinear Fokker-Planck-Kolmogorov equation. This talk is about the converse: we present a general technique how to identify a solution to a nonlinear Fokker-Planck-Kolmogorov equation consisting of probability densities as the time marginals of a solution to a distribution dependent SDE. We apply this to the special case of a porous media equation perturbed by the divergence of a vector field depending nonlinearly on the solution. More precisely, we construct a generalized entropic solution $u$ to this equation and apply the above general technique to find the corresponding distribution dependent SDE which has a weak solution with marginals given by $u$. We thus gain a probabilistic representation of $u$.
Reference: arXiv:1801.10510 |
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