An Lp-theory for stochastic partial differential equations driven by Lévy processes with pseudo-differential operators of arbitrary order

Ildoo Kim; Kyeong Hun Kim

doi:10.1016/j.spa.2016.03.001

An L_p-theory for stochastic partial differential equations driven by Lévy processes with pseudo-differential operators of arbitrary order

Ildoo Kim, Kyeong Hun Kim

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

9 Citations (Scopus)

Abstract

In this article we present uniqueness, existence, and L_p-estimates of the quasilinear stochastic partial differential equations driven by Lévy processes of the type du=(Lu+F(u))dt+G^k(u)dZ_t^k, where L is a pseudo-differential operator and Z^k are independent Lévy processes (k=1,2,⋯). The operator L is random and may depend also on time and space variables. In particular, our results include an L_p-theory of 2m-order SPDEs with coefficients measurable in (ω,t) and continuous in x.

Original language	English
Pages (from-to)	2761-2786
Number of pages	26
Journal	Stochastic Processes and their Applications
Volume	126
Issue number	9
DOIs	https://doi.org/10.1016/j.spa.2016.03.001
Publication status	Published - 2016 Sept 1

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

High-order operators
L-theory
Pseudo-differential operator
Stochastic partial differential equations driven by Lévy processes

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2016.03.001

Cite this

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title = "An Lp-theory for stochastic partial differential equations driven by L{\'e}vy processes with pseudo-differential operators of arbitrary order",

abstract = "In this article we present uniqueness, existence, and Lp-estimates of the quasilinear stochastic partial differential equations driven by L{\'e}vy processes of the type du=(Lu+F(u))dt+Gk(u)dZtk, where L is a pseudo-differential operator and Zk are independent L{\'e}vy processes (k=1,2,⋯). The operator L is random and may depend also on time and space variables. In particular, our results include an Lp-theory of 2m-order SPDEs with coefficients measurable in (ω,t) and continuous in x.",

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T1 - An Lp-theory for stochastic partial differential equations driven by Lévy processes with pseudo-differential operators of arbitrary order

AU - Kim, Ildoo

AU - Kim, Kyeong Hun

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N2 - In this article we present uniqueness, existence, and Lp-estimates of the quasilinear stochastic partial differential equations driven by Lévy processes of the type du=(Lu+F(u))dt+Gk(u)dZtk, where L is a pseudo-differential operator and Zk are independent Lévy processes (k=1,2,⋯). The operator L is random and may depend also on time and space variables. In particular, our results include an Lp-theory of 2m-order SPDEs with coefficients measurable in (ω,t) and continuous in x.

AB - In this article we present uniqueness, existence, and Lp-estimates of the quasilinear stochastic partial differential equations driven by Lévy processes of the type du=(Lu+F(u))dt+Gk(u)dZtk, where L is a pseudo-differential operator and Zk are independent Lévy processes (k=1,2,⋯). The operator L is random and may depend also on time and space variables. In particular, our results include an Lp-theory of 2m-order SPDEs with coefficients measurable in (ω,t) and continuous in x.

KW - High-order operators

KW - L-theory

KW - Pseudo-differential operator

KW - Stochastic partial differential equations driven by Lévy processes

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