SOME PROPERTIES OF SPACE-TIME FRACTIONAL STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH LÉVY NOISE

L. I. Kexue

doi:10.1216/RMJ.2021.51.1715

SOME PROPERTIES OF SPACE-TIME FRACTIONAL STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH LÉVY NOISE

L. I. Kexue

School of Mathematics and Statistics

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

Abstract

We consider a class of space-time fractional stochastic partial differential equation on a bounded domain with Lévy noise. We prove that the second moment of the solution u(t, x) can not decay exponentially and for β ∈ 0, ¹₂ , sup_x∈_D E|u(t, x)|² grows exponentially fast for large t. When β ∈ ¹₂ , 1, there is some phase transition of the second moment growth, depending on the noise level λ.

Original language	English
Pages (from-to)	1715-1722
Number of pages	8
Journal	Rocky Mountain Journal of Mathematics
Volume	51
Issue number	5
DOIs	https://doi.org/10.1216/RMJ.2021.51.1715
State	Published - Oct 2021

Keywords

And phrases: space-time fractional stochastic equations
Lévy noise
Mittag–Leffler function

Access to Document

10.1216/RMJ.2021.51.1715

Cite this

@article{95b33d8d826e47878cd7475946059c0c,

title = "SOME PROPERTIES OF SPACE-TIME FRACTIONAL STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH L{\'E}VY NOISE",

abstract = "We consider a class of space-time fractional stochastic partial differential equation on a bounded domain with L{\'e}vy noise. We prove that the second moment of the solution u(t, x) can not decay exponentially and for β ∈ 0, 12 , supx∈D E|u(t, x)|2 grows exponentially fast for large t. When β ∈ 12 , 1, there is some phase transition of the second moment growth, depending on the noise level λ.",

keywords = "And phrases: space-time fractional stochastic equations, L{\'e}vy noise, Mittag–Leffler function",

author = "Kexue, \{L. I.\}",

year = "2021",

month = oct,

doi = "10.1216/RMJ.2021.51.1715",

language = "英语",

volume = "51",

pages = "1715--1722",

journal = "Rocky Mountain Journal of Mathematics",

issn = "0035-7596",

publisher = "Rocky Mountain Mathematics Consortium",

number = "5",

}

TY - JOUR

T1 - SOME PROPERTIES OF SPACE-TIME FRACTIONAL STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH LÉVY NOISE

AU - Kexue, L. I.

PY - 2021/10

Y1 - 2021/10

N2 - We consider a class of space-time fractional stochastic partial differential equation on a bounded domain with Lévy noise. We prove that the second moment of the solution u(t, x) can not decay exponentially and for β ∈ 0, 12 , supx∈D E|u(t, x)|2 grows exponentially fast for large t. When β ∈ 12 , 1, there is some phase transition of the second moment growth, depending on the noise level λ.

AB - We consider a class of space-time fractional stochastic partial differential equation on a bounded domain with Lévy noise. We prove that the second moment of the solution u(t, x) can not decay exponentially and for β ∈ 0, 12 , supx∈D E|u(t, x)|2 grows exponentially fast for large t. When β ∈ 12 , 1, there is some phase transition of the second moment growth, depending on the noise level λ.

KW - And phrases: space-time fractional stochastic equations

KW - Lévy noise

KW - Mittag–Leffler function

UR - https://www.scopus.com/pages/publications/85126303792

U2 - 10.1216/RMJ.2021.51.1715

DO - 10.1216/RMJ.2021.51.1715

M3 - 文章

AN - SCOPUS:85126303792

SN - 0035-7596

VL - 51

SP - 1715

EP - 1722

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 5

ER -

SOME PROPERTIES OF SPACE-TIME FRACTIONAL STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH LÉVY NOISE

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this