Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise
Le Chen, Yaozhong Hu, Kamran Kalbasi, David Nualart
TL;DR
This paper investigates the stochastic heat equation driven by rough fractional Gaussian noise with Hurst parameter less than 1/2, establishing a Feynman-Kac representation and bounds for moments of the solution.
Contribution
It introduces a Feynman-Kac formula for the solution and derives matching bounds for its moments in the context of rough fractional Gaussian noise.
Findings
Established Feynman-Kac representation for the solution.
Derived matching upper and lower bounds for moments.
Analyzed the behavior of solutions driven by rough fractional noise.
Abstract
This paper studies the stochastic heat equation driven by time fractional Gaussian noise with Hurst parameter . We establish the Feynman-Kac representation of the solution and use this representation to obtain matching lower and upper bounds for the moments of the solution.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Stochastic processes and statistical mechanics