Weak error in negative Sobolev spaces for the stochastic heat equation
Omar Aboura (SAMM)
TL;DR
This paper investigates the weak error analysis of the stochastic heat equation within negative Sobolev spaces, focusing on the behavior of the error in specific functional norms.
Contribution
It advances the understanding of weak error estimates for the stochastic heat equation by analyzing errors in negative Sobolev space norms.
Findings
Provides new weak error bounds in negative Sobolev spaces
Enhances theoretical understanding of stochastic heat equation errors
Lays groundwork for improved numerical methods
Abstract
In this paper, we make another step in the study of weak error of the stochastic heat equation by considering norms as functional.
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Taxonomy
TopicsStochastic processes and financial applications · Stability and Controllability of Differential Equations · Numerical methods in inverse problems