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Local Nondeterminism and Local Times of the Stochastic Wave Equation Driven by Fractional-Colored Noise
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Local Nondeterminism and Local Times of the Stochastic Wave Equation Driven by Fractional-Colored Noise

Cheuk Yin Lee
Journal of Fourier Analysis and Applications, 卷.28(2), 26
04/2022

摘要

Local nondeterminism Local time Stochastic wave equation Analysis Mathematics (all) Applied Mathematics
We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we establish strong local nondeterminism of the solution and the existence of jointly continuous local times. We also study the differentiability and moduli of continuity of the local times and deduce some sample path properties of the solution.

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https://doi.org/10.1007/s00041-022-09914-w檢視
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