Year: 2026
Type: article
Abstract: 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 $$\ell ^p$$ 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 $$H^\infty $$ H ∞ -functional calculus, we derive a powerful discrete maximal estimate in the trace space norm $$D_A(1-\frac{1}{p},p)$$ D A ( 1 - 1 p , p ) for $$p \in [2,\infty )$$ p ∈ [ 2 , ∞ ) .
Source: Mathematische Annalen
Institution: Delft University of Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7128802876