ABSTRACT

Let { Ω , σ , P } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq1730.tif"/> be the probability space, { f t , t ⩾ 0 } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq1731.tif"/> a family of σ—algebras, f t ⊂ σ , t ∈ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq1732.tif"/> [ 0 , T ] , ξ ( t ) ∈ R m https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq1733.tif"/> be ft — adapted wiener process, Ho be set of piecewise continuous functions φ ( s ) ∈ R n , s ⩽ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq1734.tif"/> , with norm | | φ | | 2 = sup s ≤ 0 M | φ ( s ) | 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq1735.tif"/>