This is the third volume (out of four) with papers which originated during the course of the Stochastic Equations and Their Applications year at the Institute for Mathematics and Its Applications at the University of Minnesota. This volume which is directed towards researchers in applied mathematics, engineering, and physics, contains contributions by P.M. Chaikin, W.D. Dozier, H.M. Lindsay, D.A. Dawson, R. Figari, G. Papanicolaou, J. Rubinstein, K.F. Freed, S. Wang, J.F. Douglas, J. Fritz, J. Goodman, L.G. Gorostiza, D.E. Loper, P.H. Roberts, H. Osada, S. Ozawa, H. Spohn, A.S. Sznitman, and H. Tanaka.