Diffusion and Learning Models
Abstract
The notion of the diffusive nature of knowledge spreading is quite old. Much more recently, the idea that the macroeconomic innovati,on and growth come from a combination of a diffusive mechanism with a learning process has been discussed and modeled in various way,s. One should mention significant progress in this approach in economics by Robert Lucas Jr., a Nobel prize winner from the Universi,ty of Chicago, and his collaborators. This circle of ideas is not limited to macroeconomics but also appears in many studies of soci,al dynamics: learning models coming from the kinetic theory have been used in applications to social sciences, including, but not li,mited to, opinion forming, society polarization along the party lines, and wealth distribution.Such models mathematically take the f,orm of a system of a nonlinear and non-local Fokker-Planck type equation coupled with a backward in time non-local Hamilton-Jacobi t,ype equation. These equations have some common features with reaction-diffusion, population modeling and optimal control problems bu,t their precise mathematical nature require truly novel approaches. The main proposed questions concern the long time behavior of su,ch systems as they arise in social dynamics and macroeconomics. In particular, they concern the existence and stability of the balan,ced growth paths, and the dependence of the solutions on the external forcing, such astaxation and other policies.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 05, 2022
- Source ID
- N000142212174
Entities
People
- Leonid V. Ryzhik
Organizations
- Office of Naval Research
- Stanford University
- United States Navy