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

Mohammud Foondun; Mathew Joseph; Kunwoo Kim

doi:10.1007/s00440-022-01153-w

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: Contribution to journal › Article › peer-review

3 Citations (Scopus)

18 Downloads (Pure)

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	English
Pages (from-to)	553–613
Number of pages	61
Journal	Probability Theory and Related Fields
Volume	185
Issue number	1-2
Early online date	15 Jun 2022
DOIs	https://doi.org/10.1007/s00440-022-01153-w
Publication status	Published - 28 Feb 2023

Keywords

heat equation
white noise
stochastic partial differential equations
small ball

Access to Document

10.1007/s00440-022-01153-wLicence: CC BY 4.0

Foondun-etal-PTRF-2022-Small-ball-probability-estimates-for-the-Holder-semi-norm-of-the-stochastic-heat-equationFinal published version, 767 KBLicence: CC BY 4.0

Cite this

@article{7c39d554f051498b91be1b495be5c903,

title = "Small ball probability estimates for the H{\"o}lder semi-norm of the stochastic heat equation",

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 H{\"o}lder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these H{\"o}lder semi-norms. ",

keywords = "heat equation, white noise, stochastic partial differential equations, small ball",

author = "Mohammud Foondun and Mathew Joseph and Kunwoo Kim",

year = "2023",

month = feb,

day = "28",

doi = "10.1007/s00440-022-01153-w",

language = "English",

volume = "185",

pages = "553–613",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

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 - 2023/2/28

Y1 - 2023/2/28

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

U2 - 10.1007/s00440-022-01153-w

DO - 10.1007/s00440-022-01153-w

M3 - Article

SN - 0178-8051

VL - 185

SP - 553

EP - 613

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

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

Cite this