The Seventh Session, on Stochastic Differential Equations, included lectures by M. Kac, R. K. Getoor, H. P. McKean, Jr. Professor Kac discussed the physical background of Langevins equation. He essentially covered two problems a Can one find a mechanical model of a heat bath, i.e., can one find a Hamiltonian and a coupling Hamiltonian such that the statistical description of the process will agree, to a good approximation, with that derived by using the Langevins equation. b Can one justify Langevins equation on the basis of a realistic model of a heat bath. Professor Getoor discussed the relationship between Markov processes and potential theory. Professor McKeans paper entitled Propagation of Chaos for a Class of Non-Linear Parabolic Equations, describes the class of motions under consideration, indicates a method of construction for this motion and indicates a proof of the appropriate propagation chaos. Author
Prepared in cooperation with Catholic Univ., Washington, D. C. See also Rept. no. AFOSR-67-2302 dated May 66, AD-833 523.