This book presents refereed research or review articles presented at the 7th Seminar on Stochastic Analysis, Random Fields and Applications, which was held at the Centro Stefano Franscini (Monte Verit) in Ascona, Switzerland, in May 2011. The seminar mainly focused on: stochastic (partial) differential equations, especially with regard to jump processes, construction of solutions and approximations Malliavin calculus and Stein methods, and other techniques in stochastic analysis, especially chaos representations and convergence, and applications to models of interacting particle systems stochastic methods in financial models, especially models for power markets or for risk analysis, empirical estimation and approximation, stochastic control and optimal pricing. The notes of the public lecture held by Nicolas Bouleau on the fundamental question of whether there can be an excessive mathematization of the world in an economic context are also included. The book will be a valuable resource for researchers working in stochastic analysis and for professionals interested in stochastic methods in finance. Contributors: R. Balan F.E. Benth F. Biagini N. Bouleau S. Cawston C. Ceci R. Cogo G. Di Nunno R. Eden H. Eyjolfsson B. Ferrario D. Filipovic A. Gombani I. Gyngy B. Jourdain A. Kohatsu-Higa T. Lim V. Ly Vath V. Mandrekar C. Marinelli L.M. Morato H.-L. Ngo I. Nourdin G. Peccati B. Rdiger W.J. Runggaldier J.-M. Sahut M. Sbai S. Scotti S. Sjursen R. Speicher S.S. Sritharan W. Stannat P.R. Stinga S. Tappe S. Ugolini A.R.L. Valdez T. Vargiolu F. Viens L. Vostrikova M. Xu.