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Local nondeterminism and local times of the stochastic wave equation driven by fractional-colored noise
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In this paper, 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 were investigated.Abstract:
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 properties 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.read more
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Stochastic heat equation with Burgers term driven by fractional noises with two reflecting walls
TL;DR: In this article , a stochastic heat equation with Burgers term with two reflecting walls h1 and h2, driven by space-time fractional noises, is studied and the existence and uniqueness of the solution by Picard iteration scheme is established.
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Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields
Cheuk Yin Lee,Yimin Xiao +1 more
TL;DR: In this paper, a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterminism were established.
Journal ArticleDOI
Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields
TL;DR: In this paper , a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterminism were established.
References
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