This volume consists of about half of the papers presented during a three-day seminar on stochastic processes held at Northwestern University in April 1981. The aim of the seminar was to bring together a small group of kindred spirits working on stochastic processes and to provide an informal atmosphere for them to discuss their current work. We plan to hold such a seminar once a year, with slight variations in emphasis to reflect the changing concerns and interests within the field. The invited participants in this year’s seminar were J. AZEMA, R.M. BLUMENTHAL, R. CARMONA, K.L. CHUNG, R.K. GETOOR, J. JACOD, F. KNIGHT, S.OREY, A.O. PITTENGER, J. PITMAN, P. PROTTER, M.K. RAO, M. SHARPE, and J. WALSH. We thank them and other participants for the productive liveliness of the seminar. As mentioned above, the present volume is only a fragment of the work discussed at the seminar, the other papers having been already committed to otherpublications. The seminar was made possible through the enlightened support of the Air Force Office of Scientific Research, Grant No. 80-0252. We are grateful to them as well as the publisher, Birkhauser Boston, for their support and encouragement.