Computer Vision

2014 Edition
| Editors: Katsushi Ikeuchi

Stochastic Partial Differential Equations

  • Annika Lang
Reference work entry



A stochastic partial differential equation (SPDE) is a partial differential equation (PDE) with an extra stochastic term, e.g., an Itô integral. Sometimes partial differential equations, where the differential operator or the initial condition is disturbed, are also called SPDEs, but the more common term for these equations is random PDEs.


First results on SPDEs and infinite-dimensional stochastic differential equations (SDEs) appeared in the mid-1960s. Ample publications and results are due to the end 1970s and early 1980s. Here the work by Walsh [20] and Pardoux [16] should be mentioned. In the early 1990s, Da Prato and Zabczyk published their book with an infinite-dimensional approach to SPDEs driven by Wiener processes [6]. In the last years, a number of books on SPDEs were published, in particular an extension of [6] by Peszat and Zabczyk [17]. Other recent publications to be mentioned...

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Annika Lang
    • 1
  1. 1.Seminar für Angewandte Mathematik, ETH ZürichZürichSwitzerland