Summary: We consider stochastic equations in the space of formal series (an analogue of power series in a Hilbert space with no requirements of convergence). Such an equation is treated as a countable system of linear equations in a Hilbert space. The solution is defined as formal series, whose components solve the given system. Existence and uniqueness of solution is proved. The main result is a local convergence of the solution (the convergence of the solution series over a random time interval) in some particular cases. We apply this result to study classical stochastic equations in a Hilbert space with analytical coefficients, whose solutions exist only within a random time interval.
For the entire collection see [Zbl 0934.00033].