Stability of stochastic partial differential equations with infinite delays

In this paper, we study the existence and the asymptotical stability in p -th moment of mild solutions to stochastic partial differential equations with infinite delays { d x ( t ) = [ A x ( t ) + f ( t , x ( t − τ ( t ) ) ) ] d t + g ( t , x ( t − δ ( t ) ) ) d W ( t ) , t ≥ 0 , x 0 ( ⋅ ) = ξ ∈ D F 0 b ( [ m ( 0 ) , 0 ] , H ) where t − τ ( t ) , t − δ ( t ) → ∞ with delays τ ( t ) , δ ( t ) → ∞ as t → ∞ . Our method for investigating the stability of solutions is based on the fixed point theorem.