An Lp-theory of a class of stochastic equations with the random fractional Laplacian driven by Lévy processes

Kyeong Hun Kim; Panki Kim

doi:10.1016/j.spa.2012.08.001

An ^Lp-theory of a class of stochastic equations with the random fractional Laplacian driven by Lévy processes

Kyeong Hun Kim, Panki Kim

Department of Mathematics

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

18 Citations (Scopus)

Abstract

In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary Lévy processes. The driving noise can be space-time in the case of one dimensional spacial variable. We prove uniqueness and existence of such equations in Sobolev spaces. Out results cover the case when the driving noise is a space-time white noise.

Original language	English
Pages (from-to)	3921-3952
Number of pages	32
Journal	Stochastic Processes and their Applications
Volume	122
Issue number	12
DOIs	https://doi.org/10.1016/j.spa.2012.08.001
Publication status	Published - 2012 Dec

Keywords

-theory
Fractional Laplacian
Lévy noise
Lévy processes
Stochastic partial differential equations
White noise

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2012.08.001

Cite this

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title = "An Lp-theory of a class of stochastic equations with the random fractional Laplacian driven by L{\'e}vy processes",

abstract = "In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary L{\'e}vy processes. The driving noise can be space-time in the case of one dimensional spacial variable. We prove uniqueness and existence of such equations in Sobolev spaces. Out results cover the case when the driving noise is a space-time white noise.",

keywords = "-theory, Fractional Laplacian, L{\'e}vy noise, L{\'e}vy processes, Stochastic partial differential equations, White noise",

author = "Kim, {Kyeong Hun} and Panki Kim",

note = "Funding Information: The research of the authors was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0027230 ).",

year = "2012",

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AU - Kim, Kyeong Hun

AU - Kim, Panki

N1 - Funding Information: The research of the authors was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0027230 ).

PY - 2012/12

Y1 - 2012/12

N2 - In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary Lévy processes. The driving noise can be space-time in the case of one dimensional spacial variable. We prove uniqueness and existence of such equations in Sobolev spaces. Out results cover the case when the driving noise is a space-time white noise.

AB - In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary Lévy processes. The driving noise can be space-time in the case of one dimensional spacial variable. We prove uniqueness and existence of such equations in Sobolev spaces. Out results cover the case when the driving noise is a space-time white noise.

KW - -theory

KW - Fractional Laplacian

KW - Lévy noise

KW - Lévy processes

KW - Stochastic partial differential equations

KW - White noise

UR - http://www.scopus.com/inward/record.url?scp=84866014801&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2012.08.001

DO - 10.1016/j.spa.2012.08.001

M3 - Article

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VL - 122

SP - 3921

EP - 3952

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

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ER -