Stochastic parabolic partial differential equations and optimal impulsive control (Q2709256)

The stochastic partial differential equation NEWLINE\[NEWLINELu(t,x)= [\lambda(t,x)\diamond W(t)+ \eta(t, x)\diamond V(t)]\diamond u(t,x)+ \delta(t,x),NEWLINE\]NEWLINE where \(L\) is a deterministic parabolic differential operator, \(W\) Gaussian white noise, \(V\) Poisson white noise, and \(\diamond\) denotes Wick multiplication, is solved in the Kondratiev space \((S)_{-1}\) of stochastic distributions. Under suitable conditions the solution is shown to be in \(L^p\), \(p\geq 1\), and for this case an optimal impulsive control is constructed.