Stochastic equations with an unbounded operator coefficient and multiplicative noise (Q1745088)

The existence of a unique solution of the Cauchy problem for the operator stochastic differential equation \[ \frac{dX(t)}{dt}=AX(t)+B(X(t))\diamond W(t),\quad X(0)=\zeta \] is proved, where \(A\) is the generator of a semigroup of class \(C_0\) in a Hilbert space \(H\), \(B\) is in a specified class of operators (that includes some unbounded operators), \(W\) is a cylindrical Wiener process, and \(\diamond\) denotes the Wick product.