Discrete stochastic maximal regularity

In this paper, we investigate discrete regularity estimates for a broad class of temporal numerical schemes for parabolic stochastic evolution equations. We provide a characterization of discrete stochastic maximal ᵖ ℓ p -regularity in terms of its continuous counterpart, thereby establishing a unified framework that yields numerous new discrete regularity results. Moreover, as a consequence of the continuous-time theory, we establish several important properties of discrete stochastic maximal regularity such as extrapolation in the exponent p and with respect to a power weight. Furthermore, employing the H^∞ H ∞ -functional calculus, we derive a powerful discrete maximal estimate in the trace space norm DA(1-1/p,p) D A ( 1 - 1 p , p ) for p ∈ [2,∞ ) p ∈ [ 2 , ∞ ) .