# A law of large numbers for interacting diffusions via a mild formulation

@article{Bechtold2020ALO, title={A law of large numbers for interacting diffusions via a mild formulation}, author={Florian Bechtold and Fabio Coppini}, journal={arXiv: Probability}, year={2020} }

Consider a system of $n$ weakly interacting particles driven by independent Brownian motions. In many instances, it is well known that the empirical measure converges to the solution of a partial differential equation, usually called McKean-Vlasov or Fokker-Planck equation, as $n$ tends to infinity. We propose a relatively new approach to show this convergence by directly studying the stochastic partial differential equation that the empirical measure satisfies for each fixed $n$. Under a… Expand

#### 2 Citations

Uniform approximation of 2d Navier-Stokes equation by stochastic interacting particle systems

- 2020

We consider an interacting particle system modeled as a system of N stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly… Expand

Uniform Approximation of 2 Dimensional Navier-Stokes Equation by Stochastic Interacting Particle Systems

- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 2020

It is proved that the (mollified) empirical process converges, uniformly in time and space variables, to the solution of the two-dimensional Navier-Stokes equation written in vorticity form. Expand

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