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Book review

Author(s) Hornung, U. (ed.)
Kotelenez, P. (ed.)
Papanicolaou, G. (ed.)
Title Random partial differential equations
Publisher Birkhäuser
Year of publication 1991
Reviewed by Günter Vojta

The field of stochastic partial differential equations is of growing interest not only within various branches of probability theory but also in mathematical and theoretical physics and in the engineering sciences. Therefore, books on this topic are welcome. This volume represents the proceedings of a conference at the Oberwolfach Research Institute, Germany. The subjects treated include the foundations of stochastic differential equations, the theory of stochastic processes, and different applications where a variety of analytical and probabilistic tools are used. Numerical methods are scarcely described, thus it seems somewhat inappropriate to include these proceedings into a series of numerical mathematics.

The book contains 13 papers of very different length which represent more or less original contributions. There is neither an introduction into the field of random partial differential equations nor some review article, and a red thread is missing. Nevertheless, the expert can find valuable information on topics such as stochastic evolution equations in Hilbert space, nonlinear partial differential equations with white noise, martingale problems, Feynman-Kac semigroups, and Nelson diffusion. Partly, the representation is perhaps too short. An over-all index is missing. The volume is camera read from the original typescripts.

These proceedings with specialized material on a professional level can be of interest for libraries and for researchers in the fields of probability theory, functional analysis, mathematical physics, mechanics and fluid dynamics.