TL;DR
This paper provides a comprehensive proof of the exact one-point distribution formula for the KPZ equation's narrow-wedge solution, making the results accessible without prior specialized knowledge.
Contribution
It offers a self-contained, rigorous proof of the KPZ equation's exact distribution formula, expanding understanding of stochastic PDEs and integrable systems.
Findings
Complete proof of the KPZ one-point distribution formula
Accessible presentation without prior specialized knowledge
Strengthens the theoretical foundation of stochastic PDEs
Abstract
We present a complete proof of the exact formula for the one-point distribution for the narrow-wedge Hopf-Cole solution to the Kardar-Parisi-Zhang (KPZ) equation. This presentation is intended to be self-contained so no previous knowledge about stochastic PDEs, or exactly solvable systems is presumed.
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Taxonomy
TopicsStochastic processes and financial applications · Random Matrices and Applications · Financial Risk and Volatility Modeling