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Contents of PMS, Vol. 19, Fasc. 2,
pages 267 - 286
 

INTERACTING PARTICLE APPROXIMATION FOR NONLOCAL QUADRATIC EVOLUTION PROBLEMS

Piotr Biler
Tadahisa Funaki
Wojbor A. Woyczyński

Abstract: The existence of McKean’s nonlinear jump Markov processes and related Monte Carlo type approximation schemes by interacting particle systems (propagation of chaos) are studied for a class of multidimensional doubly nonlocal evolution problems with a fractional power of the Laplacian and a quadratic nonlinearity involving an integral operator. Asymptotically, these equations model the evolution of density of mutually interacting particles with anomalous (fractal) Lévy diffusion.

1991 AMS Mathematics Subject Classification: 35K60, 60H, 82C21.

Key words and phrases: nonlinear nonlocal parabolic equations, fractal anomalous diffusion, McKean’s diffusions, interacting particle systems, propagation of chaos.

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