An averaging principle for stochastic evolution equations. (English) Zbl 0718.60068

Seidler, Jan; Vrkoč, Ivo

Čas. Pěstování Mat. 115, No. 3, 240-263 (1990).

Summary: Integral continuity theorems for solutions of stochastic partial differential equations of evolution type with small parameter are established. These equations are treated in the framework of the semigroup approach, the equations driven by a Wiener process with nuclear incremental covariance operator, those driven by a cylindrical process and the equations of DaPrato-Zabczyk’s type [C. DaPrato and J. Zabczyk, Differ. Integral Equ. 1, 143-155 (1988)] being investigated parallelly. As a preliminary result, a fairly general existence theorem for the equations driven by the cylindrical Wiener process is established.

MSC:

60H15

Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

infinite-dimensional Wiener process; Integral continuity theorems; stochastic partial differential equations