Sample Paths of the Solution to the ...
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Pré-publication ou Document de travail
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Title :
Sample Paths of the Solution to the Fractional-colored Stochastic Heat Equation
Author(s) :
English keyword(s) :
law of the iterated logarithm
fractional Brownian motion
Stochastic heat equation
Gaussian noise
path regularity
fractional Brownian motion
Stochastic heat equation
Gaussian noise
path regularity
HAL domain(s) :
Mathématiques [math]/Probabilités [math.PR]
English abstract : [en]
Let u = {u(t, x), t ∈ [0, T ], x ∈ R d } be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with ...
Show more >Let u = {u(t, x), t ∈ [0, T ], x ∈ R d } be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with respect to the time and space variable, respectively. In particular, we derive their exact uniform and local moduli of continuity and Chung-type laws of the iterated logarithm.Show less >
Show more >Let u = {u(t, x), t ∈ [0, T ], x ∈ R d } be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with respect to the time and space variable, respectively. In particular, we derive their exact uniform and local moduli of continuity and Chung-type laws of the iterated logarithm.Show less >
Language :
Anglais
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Submission date :
2025-01-24T18:27:49Z
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