This volume contains 20 refereed research or review papers presented at the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from September 20 to 24, 1999. The seminar focused on three topics: fundamental aspects of stochastic analysis, physical modeling, and applications to financial engineering. The third topic was the subject of a mini-symposium on stochastic methods in financial models.

Light, atoms, and singularities.- How random are random walks ?.- Classical solutions for SPDEs with Dirichlet boundary conditions.- Credit Risk: The structural approach revisited.- Classical solutions for Kolmogorov equations in Hilbert spaces.- Monotone gradient systems in L2spaces.- Catalytic and mutually catalytic super-brownian motions.- Sticky particles, scalar conservation law and pressureless gas equations.- Affine short rate models.- A filtered EM algorithm for parameter estimation in linear filtering.- Instability of a quantum particle induced by a randomly varying spring coefficient.- On the superreplication approach for European interest rates derivatives.- A complete market model with Poisson and Brownian components.- Stochastic calculus and processes in non-commutative space-time.- A measure-valued process related to the parabolic Anderson model.- Homogenization of PDEs with non linear boundary condition.- A Bayesian adaptative control approach to risk management in a binomial model.- Hölder continuity for the stochastic heat equation with spatially correlated noise.- Regularity conditions for parabolic SPDEs on Lie groups.- Forward integrals and stochastic differential equations.