Asymptotics and high dimensional approximations for nonlinear pseudodifferential equations involving Lévy generators (Q2732358)

The authors present several results concerning asymptotics and high dimensional Monte Carlo-type approximations via interacting particle systems for the Cauchy problem for nonlinear pseudodifferential equations of the form \(u_t+{\mathcal L}u +\nabla {\mathcal N}u=0\) (generalizations of the Burgers equation), where \(u:\mathbb{R}^d\times \mathbb{R}_+\to\mathbb{R}\), \(-{\mathcal L}\) is a (linear) generator of a symmetric positive semigroup \(e^{-t{\mathcal L}}\) on \(L^1 (\mathbb{R}^d)\), with the symbol defined by the Lévy-Khintchine formula [see \textit{J. Bertoin}, Lévy processes (Cambridge University Press, Cambridge) (1996; Zbl 0861.60003), Ch. 1, Th. 1] and \({\mathcal N}\) is a nonlinear operators. The proof will appear elswehere.