Infinite dimensional stochastic differential equations of Ornstein–Uhlenbeck type

AbstractWe consider the operatorLf(x)=12∑i,j=1∞aij(x)∂2f∂xi∂xj(x)-∑i=1∞λixibi(x)∂f∂xi(x).We prove existence and uniqueness of solutions to the martingale problem for this operator under appropriate conditions on the aij,bi, and λi. The process corresponding to L solves an infinite dimensional stochastic differential equation similar to that for the infinite dimensional Ornstein–Uhlenbeck process