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, P. Hsu, J.-F. Le Gall, M. Liao, P. March, P. McGill, J. Mitro, T. Mountford, C. Mueller, A. Mukherjea, V. Papanicolaou, E. Perkins, M. Pinsky, L. Pitt, A. O. Pittenger, Z. Pop-Stojanovic, M. Rao, J. Rosen, T. Salisbury, C. Shih, M. Taksar, J. Taylor, S. J. Taylor, E. Toby, R. Williams, Wu Rong, and Z. Zhao. The seminar was made possible through the generous support of the Department of Mathematics, the Center for Applied Mathematics, the Division of Sponsored Research and the College of Liberal Arts and Sciences of the University of Florida. We extend our thanks for local arrangements to our host, Zoran Pop-Stojanovic. 1. G.

The Riesz Transform Associated with Second Order Differential Operators.- The Optional Stochastic Integral.- On Brownian Excursions in Lipschitz Domains II: Local Asymptotic Distributions.- Gauge Theorem for Unbounded Domains.- Reminiscences of Some of Paul Levy's Ideas in Brownian Motion and in Markov Chains.- Conditional Brownian Motion, Whitney Squares, and the Conditional Gauge Theorem.- Local Field Gaussian Measures.- Some Formulas for the Energy Functional of a Markov Process.- Note on the 3G Theorem (d=2).- The Independence of Hitting Times and Hitting Positions to Spheres for Drifted Brownian Motion.- The Exact Hausdorff Measure of Brownian Multiple Points II.- On a Stability Property of Harmonic Measures.- Behavior of Excessive Functions of Certain Diffusions Under the Action of the Transition Semigroup.- A Maximal Inequality.- Some Results for Functions of Kato Class in Domains of Infinite Measure.- Some Properties of Invariant Functions of Markov Processes.- Right Brownian Motion and Representation of Initial Problem.