Applied Mathematics & Information Sciences

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This paper deals with a further generalization of the continuous thermostatted kinetic theory for active particles. Specifically the interest focuses on the linking between the macroscopic data and the statistical evolution of the system. The connection between measurements and sources is established by defining an inverse problem based on the distribution vector function solution of the thermostatted kinetic framework. The inverse problem belongs to the class of ill-posed Volterra equations of the first kind considering that the number of sources can be greater of the number of measurements. The uniqueness of the solution is obtained by coupling the thermostatted kinetic theory with the information theory and more precisely with themaximum entropy principle of Jayne. Applications, which are discussed into the last section of the paper, refer to biological systems, vehicular traffic, crowds dynamics, and finance.

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