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From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE
- Publication Year :
- 2018
-
Abstract
- We construct weak solutions to a class of distribution dependent SDE, of type $dX(t)=b\left( X(t), \displaystyle\frac{d\mathcal{L}_{X(t)}}{dx}(X(t))\right) dt+\sigma\left( X(t),\displaystyle\frac{d\mathcal{L}_{X(t)}}{dt}(X(t))\right) dW(t)$ for possibly degenerate diffusion matrices $\sigma$ with $X(0)$ having a given law, which has a density with respect to Lebesgue measure, $dx$. Here ${\mathcal{L}}_{X(t)}$ denotes the law of $X(t)$. Our approach is to first solve the corresponding nonlinear Fokker-Planck equations and then use the well known superposition principle to obtain weak solutions of the above SDE.
- Subjects :
- Mathematics - Probability
60H30, 60H10, 60G46, 35C99, 58J165
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1808.10706
- Document Type :
- Working Paper