Abstract

Let be a sequence of identically distributed, weakly independent and weakly Gaussian cylindrical random variables in a separable Banach space . We consider the cylindrical difference equation, , in and determine a cylindrical process which solves the equation. The cylindrical distribution of is shown to be weakly Gaussian and independent of . It is also shown to be strongly Gaussian if the cylindrical distribution of is strongly Gaussian. We determine the characteristic functional of and give conditions under which is unique.

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