Pointwise upper bound for the fundamental solution of fractional Fokker-Planck equation
Haina Li, Yiran Xu
TL;DR
This paper establishes a pointwise upper bound for the fundamental solution of the fractional Fokker-Planck equation using Littlewood-Paley decomposition, providing a concise proof of the estimate.
Contribution
It introduces a novel application of Littlewood-Paley decomposition to derive pointwise bounds for the fundamental solution of the fractional Fokker-Planck equation.
Findings
Derived a pointwise upper bound for the fundamental solution.
Provided a concise proof leveraging Littlewood-Paley decomposition.
Enhanced understanding of the fundamental solution's behavior.
Abstract
In this paper, we investigate the fundamental solution of the fractional Fokker-Planck equation. Utilizing the Littlewood-Paley decomposition technology, we present a concise proof of the pointwise estimate for the fundamental solution.
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Taxonomy
TopicsFractional Differential Equations Solutions · Statistical Mechanics and Entropy · Stochastic processes and financial applications