This volume contains twenty refereed research or review papers presented at the 4th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verita ) in Ascona, Switzerland, from May 19 to 24, 2002. The seminar focused mainly on stochastic partial differential equations, stochastic models in mathematical physics, and financial engineering. The book will be a valuable resource for both researchers in stochastic analysis and professionals interested in stochastic methods in finance and insurance. Contributors: R. J. Adler, X. Bardina, J. Bertoin, P. Biane, A. B. Cruzeiro, J. A. Cuesta-Albertos, R. C. Dalang, I. M. Davies, S. Deparis, M. A. Diop, E. Eberlein, F. Flandoli, J. -P. Fouque, M. Gubinelli, E. A. v. Hammerstein, P. Imkeller, S. Kwapien, R. Landre, P. Lescot, O. Lavaque, D. Marquez-Carreras, C. Martini, A. Mira, G. Papanicolaou, E. Pardoux, I. Pavlyukevich, M.-C. Quenez, J. Rosinski, C. Rovira, R. Sircar, C. Stricker, P. Tenconi, S. Tindel, A. Truman, M. Wschebor, M. Yor, J.-C. Zambrini, X. Zhang, H. Zhao