INTERACTING PARTICLE APPROXIMATION FOR NONLOCAL
QUADRATIC EVOLUTION PROBLEMS
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.