Considerations on the Controllability of Stochastic Linear Heat Equations

Recently some interest (see [1], [7] and [14]) has been attracted by the controllability problem for a forward stochastic controlled heat equation as: (1) { d s y ( s , ξ ) = ( Δ ξ y ( s , ξ ) + a ( ξ ) y ( s , ξ ) + I O ( ξ ) u ( s , ξ ) ) d s +                                                                                                                                                                           + c ( ξ ) y ( s , ξ ) d β s ,         in   [ t , T ] × D y ( s , ξ ) = 0 ,           on   [ t , T ] × ∂ D y ( t , ξ ) = x ( ξ ) ,           in     D https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203910177/0082baec-0164-4123-9297-401a14f7d1e0/content/eq290.tif"/>