TY - JOUR
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
N1 - Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A2055538 ).
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/9/1
Y1 - 2016/9/1
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
UR - http://www.scopus.com/inward/record.url?scp=84961774317&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2016.03.001
DO - 10.1016/j.spa.2016.03.001
M3 - Article
AN - SCOPUS:84961774317
SN - 0304-4149
VL - 126
SP - 2761
EP - 2786
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 9
ER -