Kolmogorov equation for solutions of Cauchy problems for a class of linear evolution equations (Q1114858)

The author considers the Cauchy problem \[ u(t,x)=\phi (x)+\int^{t}_{s}D_ 1(r)u(r,x)dr+\int^{t}_{s}D_ 2(r)u(r,x)dW(r), \] in the region \([s,T]\times R^ n\), where W(t) is a Wiener process and \(D_ 1\), \(D_ 2\) are second order differential operators. The dependences of the solutions of the above equations on initial conditions s and \(\phi\) is studied.