A Class of Markov Processes Associated With Nonlinear Parabolic Equations

Introduction.-Thefamiliar connection between the Brownian motion and the differential operator f -> f"/2, based upon the fact that the Brownian transition function (27rt)-1' exp-(b -a)2/2t is also the elementary solution of bu/bt = (1/2)(2U/oa2, is. the simplest and most fruitful instance of the connection between Markov processes with constant transition mechanism and linear parabolic equations.The purpose of this paper is to explain a similar connection between a wider class of Markov processes and certain nonlinear parabolic equations.Boltzmann's equation from statistical mechanics is a special case, as is Burgers' equation: au/at = (1/2)2u/oa2 -ubu/ba.1. Markov Processes with Constant Transition Mechanism.-Givena nice