Some remarks on boundary value problems for linear stochastic differential equations (Q1109420)

The authors consider the linear stochastic differential equation \[ dx_ t=(A(t)x_ t+a(t))dt+(B_ i(t)x_ t+b_ i(t))dw\quad i_ t \] with condition \(Lx=y\), L:L \(2(\Omega,F_ T,C(O,T))\to L\) \(2(\Omega,F_ T)\), on the probability space \((\Omega,F,(F_ t)_{t\geq 0},P)\). It is shown that the set of y solving the above equation is nowhere dense in L \(2(\Omega,F_ T)\).