Hochschild Cohomology Theories in White Noise Analysis
R\'emi L\'eandre
TL;DR
This paper demonstrates that the continuous and differential Hochschild cohomology theories coincide for the Hida test algebra with the normalized Wick product, advancing understanding in white noise analysis.
Contribution
It establishes the equivalence of two Hochschild cohomology theories within the context of white noise analysis, specifically for the Hida test algebra.
Findings
Continuous and differential Hochschild cohomologies are identical for the Hida test algebra.
The result simplifies the cohomological analysis in white noise spaces.
Advances theoretical understanding of algebraic structures in stochastic analysis.
Abstract
We show that the continuous Hochschild cohomology and the differential Hochschild cohomology of the Hida test algebra endowed with the normalized Wick product are the same.
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