The 1988 Seminar on Stochastic Processes was held at the University of Florida, Gainesville, March 3 through March 5, 1988. It was the eighth 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 Princeton University, Northwestern University, the University of Florida and the University of Virginia. The participants' enthusiasm and interest have created stimulating and successful seminars. We thank those participants who have permitted us to publish their research in this volume. This year's invited participants included B. Atkinson, J. Azema, D. Bakry, P. Baxendale, J. Brooks, G. Brosamler, K. Burdzy, E. Cinlar, R. Darling, N. Dinculeanu, E. Dynkin, S. Evans, N. Falkner, P. Fitzsimmons, R. Getoor, J. Glover, V. Goodman,