ABSTRACT
As mentioned at the end of §1.1, the white noise B ˙ ( t ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203733813/e9279b26-91e9-40dd-8029-b908c0f36f6c/content/eq125.tif"/> is a generalized function on an infinite dimensional space. First we shall specify such a space. A common choice is the Schwartz space S ( ℝ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203733813/e9279b26-91e9-40dd-8029-b908c0f36f6c/content/eq126.tif"/> of real-valued rapidly decreasing functions on ℝ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203733813/e9279b26-91e9-40dd-8029-b908c0f36f6c/content/eq127.tif"/> . A function ξ on ℝ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203733813/e9279b26-91e9-40dd-8029-b908c0f36f6c/content/eq128.tif"/> is called rapidly decreasing if it is smooth and for all nonnegative integers n and k, | x n ξ ( k ) ( x ) | → 0 as | x | → ∞ . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203733813/e9279b26-91e9-40dd-8029-b908c0f36f6c/content/eq129.tif"/>
