The 1987 Seminar on Stochastic Processes was held at Princeton University, March 26 through March 28, 1987. It was the seventh seminar in a continuing series of meetings which provide opportunities for researchers to discuss current work in stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Evanston; University of Florida, Gainesville: and University of Virginia, Charlottesville. The success of these seminars has been due to the interest and enthusiasm of probabilists in the United States and abroad. Many of the participants have allowed us to pUblish the results of their re search in this volume. The editors hope that the reader will be able to sense some of the excitement present in the seminar by reading these articles. This year's invited participants included M. Aizenman, B. Atkinson, R. M. Blumenthal, C. Burdzy, D. Burkholder, R. Carmona, K. L. Chung, M. Cranston, C. Dellacherie, J. D. Deuschel, N. Dinculeanu, Gundy, P. Hsu, E. B. Dynkin, P. Fitzsimmons, R. K. Getoor, J. Glover, R. G. Hunt, H. Kaspi, Knight, G. Lawler, P. March, P. A. Meyer, A. F. J. Mitro, J. Neveu, E. Pardoux, M. Pinsky, L. Pitt, A. O. Pittenger, Z. Pop-Stojanovic, P. Protter, M. Rao, T. Salisbury, M. J. Sharpe, S. J. Taylor, E. Toby, S. R. S. Varadhan, R. Williams, M. Weber, and Z. Zhao.