Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

Prakash Chakraborty; Xia Chen; Bo Gao; Samy Tindel

doi:10.1016/j.spa.2020.06.007

Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

Prakash Chakraborty, Xia Chen, Bo Gao, Samy Tindel

Harold and Inge Marcus Department of Industrial and Manufacturing Engineering

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise Ẇ in space. We consider the case [Formula presented] and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman–Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form [Formula presented].

Original language	English (US)
Pages (from-to)	6689-6732
Number of pages	44
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	11
DOIs	https://doi.org/10.1016/j.spa.2020.06.007
State	Published - Nov 2020

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2020.06.007

Cite this

@article{ebdd747cb0ba4ac4947b0f725cafa791,

title = "Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise",

abstract = "In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise Ẇ in space. We consider the case [Formula presented] and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman–Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form [Formula presented].",

author = "Prakash Chakraborty and Xia Chen and Bo Gao and Samy Tindel",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

month = nov,

doi = "10.1016/j.spa.2020.06.007",

language = "English (US)",

volume = "130",

pages = "6689--6732",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "11",

}

TY - JOUR

T1 - Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

AU - Chakraborty, Prakash

AU - Chen, Xia

AU - Gao, Bo

AU - Tindel, Samy

PY - 2020/11

Y1 - 2020/11

N2 - In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise Ẇ in space. We consider the case [Formula presented] and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman–Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form [Formula presented].

AB - In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise Ẇ in space. We consider the case [Formula presented] and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman–Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form [Formula presented].

UR - https://www.scopus.com/pages/publications/85087402757

UR - https://www.scopus.com/inward/citedby.url?scp=85087402757&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2020.06.007

DO - 10.1016/j.spa.2020.06.007

M3 - Article

AN - SCOPUS:85087402757

SN - 0304-4149

VL - 130

SP - 6689

EP - 6732

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 11

ER -

Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this