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This is the seventh volume (out of a projected ten) with papers which appeared during the "Stochastic Equations and Their Applications" year (1985-1986) at the Institute for Mathematics and its Applications at the University of Minnesota. This volume is directed towards researchers in applied mathematics, engineering, and physics and contains contributions by: J. R. Baxter, N. C. Jain, L. Bonilla, R. Burridge, G. Papanicolaou, B. White, R. Carmona, P. L. Chow, M. H. Cohen, R. T. Durrett, W. Faris, B. Gidas, J. Imbrie, J. Klauder, J. Keller, W. Kohler, S. Kotani, W. P. Peterson, M. A. Pinsky, B. Simon, H. Soner, B. Souillard, V. Twersky, and B. S. White.