A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C 1-domains

Kyeong Hun Kim

doi:10.1016/j.spa.2013.08.008

A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on ^{C 1}-domains

Kyeong Hun Kim

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

3 Citations (Scopus)

Abstract

In this paper we study parabolic stochastic partial differential equations (SPDEs) driven by Lévy processes defined on R^d, R+d and bounded ^C1-domains. The coefficients of the equations are random functions depending on time and space variables. Existence and uniqueness results are proved in (weighted) Sobolev spaces, and ^Lp-estimates and various properties of solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular it can be negative or fractional.

Original language	English
Pages (from-to)	440-474
Number of pages	35
Journal	Stochastic Processes and their Applications
Volume	124
Issue number	1
DOIs	https://doi.org/10.1016/j.spa.2013.08.008
Publication status	Published - 2014

Bibliographical note

Funding Information:
The research of the author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2013020522 ).

Keywords

-theory
Lévy processes
Sobolev spaces
Stochastic partial differential equations

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2013.08.008

Cite this

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title = "A Sobolev space theory for parabolic stochastic PDEs driven by L{\'e}vy processes on C 1-domains",

abstract = "In this paper we study parabolic stochastic partial differential equations (SPDEs) driven by L{\'e}vy processes defined on Rd, R+d and bounded C1-domains. The coefficients of the equations are random functions depending on time and space variables. Existence and uniqueness results are proved in (weighted) Sobolev spaces, and Lp-estimates and various properties of solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular it can be negative or fractional.",

keywords = "-theory, L{\'e}vy processes, Sobolev spaces, Stochastic partial differential equations",

author = "Kim, {Kyeong Hun}",

note = "Funding Information: The research of the author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2013020522 ).",

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T1 - A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C 1-domains

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N1 - Funding Information: The research of the author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2013020522 ).

PY - 2014

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N2 - In this paper we study parabolic stochastic partial differential equations (SPDEs) driven by Lévy processes defined on Rd, R+d and bounded C1-domains. The coefficients of the equations are random functions depending on time and space variables. Existence and uniqueness results are proved in (weighted) Sobolev spaces, and Lp-estimates and various properties of solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular it can be negative or fractional.

AB - In this paper we study parabolic stochastic partial differential equations (SPDEs) driven by Lévy processes defined on Rd, R+d and bounded C1-domains. The coefficients of the equations are random functions depending on time and space variables. Existence and uniqueness results are proved in (weighted) Sobolev spaces, and Lp-estimates and various properties of solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular it can be negative or fractional.

KW - -theory

KW - Lévy processes

KW - Sobolev spaces

KW - Stochastic partial differential equations

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JF - Stochastic Processes and their Applications

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