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Discrete stochastic maximal regularity.

Foivos Evangelopoulos-Ntemiris1, Mark Veraar1

  • 1Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.

Mathematische Annalen
|February 16, 2026
PubMed
Summary

This study introduces a unified framework for discrete regularity estimates in parabolic stochastic evolution equations. It establishes new discrete stochastic maximal regularity results and properties, enhancing numerical analysis for these equations.

Keywords:
42B3747D0660H1560H3565J1065M12Primary 46N40Secondary 35B65

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Area of Science:

  • Numerical Analysis
  • Stochastic Partial Differential Equations
  • Functional Analysis

Background:

  • Parabolic stochastic evolution equations are crucial in modeling complex systems.
  • Understanding discrete regularity is essential for accurate numerical simulations.
  • Existing methods lack a unified framework for discrete stochastic maximal regularity.

Purpose of the Study:

  • To develop a unified framework for discrete regularity estimates.
  • To characterize discrete stochastic maximal $\ell^p$-regularity.
  • To establish new discrete regularity results and properties for numerical schemes.

Main Methods:

  • Characterization of discrete stochastic maximal $\ell^p$-regularity.
  • Utilizing continuous-time theory for discrete properties.
  • $H^\infty$-functional calculus for trace space norm estimates.

Main Results:

  • A unified framework for discrete regularity estimates is established.
  • New discrete stochastic maximal regularity results are derived.
  • Properties like extrapolation in exponent p and power weight are proven.

Conclusions:

  • The findings provide a robust theoretical foundation for numerical schemes of parabolic stochastic evolution equations.
  • The unified framework simplifies and expands the study of discrete regularity.
  • The derived estimates offer improved accuracy and applicability in simulations.