Diffusing particles with electrostatic repulsion
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We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see ), and then we consider the behaviour of this system when the number of particles $N$ goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as $N \uparrow \infty$ ) is partly similar to that of T. Chan  and L.C.G. Rogers - Z. Shi , except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE.
- Diffusing particles with electrostatic repulsion
Probability Theory and Related Fields
Volume 107, Issue 4 , pp 429-449
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- Mathematics Subject Classification (1991): 60K35, 60F05, 60H10, 60J60
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