Convergence of solution of stochastic equations in formal series (Q2711785)

The author considers stochastic differential equations in the space of formal power series with coefficients from a Hilbert space. Such an equation is treated as a countable system of linear equations in a Hilbert space. Existence and uniqueness of a solution are proved. The main result is a local convergence of solutions, that is convergence of the solution series in a random time interval, under some assumptions regarding coefficients of the equation. This is applied to classical stochastic equations in a Hilbert space with a linear diffusion and analytic drift (without growth restrictions) whose solutions exist only within a random time interval.