Abstract
We consider a general nonlinear kinetic type equation that can describe the time evolution of a variable related to an economical state of an individual agent of the system. We assume asymmetric interactions between the agents. We show that in a corresponding limit, it is asymptotically equivalent to a nonlinear inviscid Burgers type equation.
Highlights
We are dealing with a kinetic theory approach to modeling complex systems in the economy
The asymmetric interaction plays an essential role in the description of phenomena in Mathematical Economy
The present paper is a first step in the description of such mathematical phenomena and, as we believe, will lead to further interesting research
Summary
We are dealing with a kinetic theory approach to modeling complex systems in the economy. In reference [8], the methods of mesoscopic kinetic equations were applied to model interactions of risky assets in a portfolio. We consider a general nonlinear kinetic type equation that can describe the time evolution of a variable related to an economical state of an individual agent of the system. The function f (t, v) describes the probability density to find an agent at the instant of time t > 0 with state v ∈ Ω, where Ω is a domain in Rd. We consider the following general class of mesoscopic equations:. The modeling process leads to the proper choice of the function T f that may depend on state distribution f Such a form of general equations was proposed in reference [18].
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