Stochastic Partial Differential Equations
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  and Pardoux  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 . In the last years, a number of books on SPDEs were published, in particular an extension of  by Peszat and Zabczyk . Other recent publications to be mentioned...
- 3.Chow P-L (2007) Stochastic partial differential equations. Applied mathematics and nonlinear science series. Chapman & Hall/CRC, Boca RatonGoogle Scholar
- 5.Dellacherie C, Meyer P-A (1978) Probabilities and potential (Transl. from the French.) North-Holland mathematics studies, vol 29. North-Holland, Amsterdam/New York/OxfordGoogle Scholar
- 6.Da Prato G, Zabczyk J (1992) Stochastic equations in infinite dimensions. Encyclopedia of mathematics and its applications, vol 44. Cambridge University Press, CambridgeGoogle Scholar
- 7.Fishman GS (1996) Monte Carlo. Concepts, algorithms, and applications. Springer, New YorkGoogle Scholar
- 8.Holden H, Øksendal B, Ubøe J, Zhang T (2010) Stochastic partial differential equations. A modeling, white noise functional approach. Universitext, 2nd edn. Springer, New YorkGoogle Scholar
- 9.Ikeda N, Watanabe S (1989) Stochastic differential equations and diffusion processes. North-Holland mathematical library, 2nd edn., vol 24. North-Holland, Amsterdam/Kodansha, TokyoGoogle Scholar
- 11.Kloeden PE, Platen E (1992) Numerical solution of stochastic differential equations. Applications of mathematics, vol 23. Springer, BerlinGoogle Scholar
- 12.. Lang A (2007) Simulation of stochastic partial differential equations and stochastic active contours. PhD thesis, Universität MannheimGoogle Scholar
- 14.Métivier M (1982) Semimartingales: a course on stochastic processes. de Gruyter studies in mathematics, vol 2. Walter de Gruyter, Berlin/New YorkGoogle Scholar
- 15.Øksendal B (2003) Stochastic differential equations. An introduction with applications. Universitext, 6th edn. Springer, BerlinGoogle Scholar
- 17.Peszat S, Zabczyk J (2007) Stochastic partial differential equations with lévy noise. An evolution equation approach. Encyclopedia of mathematics and its applications, vol 113. Cambridge University Press, CambridgeGoogle Scholar
- 18.Prévôt C, Röckner M (2007) A concise course on stochastic partial differential equations. Lecture notes in mathematics, vol 1905. Springer, BerlinGoogle Scholar
- 19.Protter PE (2004) Stochastic integration and differential equations. Applications of mathematics, 2nd edn., vol 21. Springer, BerlinGoogle Scholar