49 research outputs found
Nonlinear L\'evy and nonlinear Feller processes: an analytic introduction
The program of studying general nonlinear Markov processes was put forward in
V. N. Kolokoltsov "Nonlinear Markov Semigroups and Interacting L\'evy Type
Processes" (Journ. Stat. Physics 126:3 (2007), 585-642), and was developed by
the author in monograph "Nonlinear Markov processes and kinetic equations".
Cambridge University Press, 2010, where, in particular, nonlinear L\'evy
processes were introduced.
The present paper is an invitation to the rapidly developing topic of
noninear Markov processes. We provide a quick (and at the same time more
abstract) introduction to the basic analytical aspects of the theory developed
in Part II of the above mentioned book.Comment: 20 page
Mean field game model of corruption
A simple model of corruption that takes into account the effect of the
interaction of a large number of agents by both rational decision making and
myopic behavior is developed. Its stationary version turns out to be a rare
example of an exactly solvable model of mean-field-game type. The results show
clearly how the presence of interaction (including social norms) influences the
spread of corruption