Preface Appl Math Optim 54:263–264 (2006) DOI: 10.1007/s00245-006-0870-5 2006 Springer Science+Business Media, Inc. Stochastic partial differential equations (SPDEs) are coming of age. The initial progress that essentially defined SPDEs as a field was done in the 1970s by a handful of people, including N. Krylov, E. Pardoux, M. Viot, and J. Walsh. Since then the field has grown substantially. By some estimates, hundreds of mathematicians as well as representatives of various sciences and engineering are now actively involved in SPDEs. The development of SPDEs has been heavily influenced by other fields of mathemat- ics (PDEs, interacting particle systems, nonlinear filtering, branching processes) as well as by sciences and engineering (turbulence, polymers, continuum physics, Euclidean quantum field theory, etc.) Most of the work done in the 1970s and 1980s had a theoretical flavor, which is quite understandable. Since the end of the 1980s, papers on numerical methods for SPDEs were published only sporadically. Mostly, these papers built on the ideas and methodology already developed for ordinary stochastic differential equations. This trickle of papers eventually developed in to a larger stream that became a new field by itself. A number of new approaches were introduced that were specific to SPDEs, and some Applied Mathematics and Optimization Springer Journals

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Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
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