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We study certain nonlinear continuous models of opinion formation derived from a kinetic description involving exchanges of opinion between individual agents. These models imply that the only possible final opinions are the extremal ones, and they are similar to models of pure drift in magnetization. Both analytical and numerical methods allow us to recover the final distribution of opinion between the two extremal ones. INDAM project "Kinetic Innovative Models for the Study of the Behavior of Fluids in Micro/Nano Electromechanical Systems," Italian M.I.U.R. project "Mathematical Problems of Kinetic Theories," and Italian M.I.U.R. project "Numerical Modelling for Scientific Computing and Advanced Applications."

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The apparatus of characteristic functions, from the time of its successful use by A. M. Lyapunov to the present, has remained one of the fundamental analytical methods of probability theory. However, although it is very convenient in the investigation of questions of an additive character (i.e., where we deal with sums of random variables), it is little suited for use in problems in which we encounter products and ratios of random variables. In addition, the apparatus of the Mellin-Stieltjes transform is well suited for problems of the second kind.I consider it my duty to thank Yu. V. Prokhorov who read the manuscript and made a number of valuable suggestions.

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