Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation

Mohammud Foondun; Mathew Joseph; Kunwoo Kim

Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation

Mohammud Foondun, Mathew Joseph, Kunwoo Kim

Mathematics And Statistics

Research output: Working paper › Working Paper/Preprint

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Abstract

We consider the stochastic heat equation on [0, 1] with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball probabilities for the Hölder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these Hölder semi-norms.

Original language	Undefined/Unknown
Place of Publication	Ithaca, New York
Number of pages	47
Publication status	Published - 2 Aug 2021

Keywords

heat equation
white noise
stochastic partial differential equations
small ball

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Foondun-etal-arXiv-2021-Small-ball-probability-estimates-for-the-Hölder-semi-norm-of-the-stochastic-heat-equationFinal published version, 680 KBLicence: CC BY 4.0

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T1 - Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation

AU - Foondun, Mohammud

AU - Joseph, Mathew

AU - Kim, Kunwoo

PY - 2021/8/2

Y1 - 2021/8/2

N2 - We consider the stochastic heat equation on [0, 1] with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball probabilities for the Hölder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these Hölder semi-norms.

AB - We consider the stochastic heat equation on [0, 1] with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball probabilities for the Hölder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these Hölder semi-norms.

KW - heat equation

KW - white noise

KW - stochastic partial differential equations

KW - small ball

UR - https://arxiv.org/abs/2108.00881v1

M3 - Working Paper/Preprint

BT - Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation

CY - Ithaca, New York

ER -

Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation

Abstract

Keywords

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Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation

Cite this