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Zbl 0608.60060
Walsh, John B.
An introduction to stochastic partial differential equations. (English)
[A] École d'été de probabilités de Saint-Flour XIV - 1984, Lect. Notes Math. 1180, 265-437 (1986).

[For the entire collection see Zbl 0579.00013.] \par This introduction to stochastic partial differential equations (SPDE's) is based on multiparameter processes. Accordingly, the Brownian sheet and martingale measures are the stochastic driving terms of the SPDE's, with a particular emphasis on space-time white noise (Brownian sheet) and its generalization to martingale measures. Apart from interesting applications the paper deals with integration theory (w.r.t. martingale measures), weak convergence of SPDE's, regularity of solutions, distribution valued solutions, and the space-time Markov property.
[P.Kotelenez]

MSC 2000:: *60H15 Stochastic partial differential equations
60G60 Random fields

Keywords: multiparameter processes; Brownian sheet; martingale measures; space-time Markov property

Citations: Zbl 0579.00013

Cited in: Zbl 1234.60064 Zbl 1108.60057 Zbl 1085.60042 Zbl 1074.60067 Zbl 1006.60059 Zbl 0998.60066 Zbl 0908.60001 Zbl 0891.60074 Zbl 0842.60063 Zbl 0836.60062 Zbl 0778.60054 Zbl 0770.60049 Zbl 0694.60041 Zbl 0713.62094

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