TY - JOUR
T1 - Reflected rough differential equations
AU - Aida, Shigeki
N1 - Funding Information:
This research was partially supported by Grant-in-Aid for Scientific Research (B) No. 24340023 . The author would like to thank the referee for the valuable comments and suggestions which improve the quality of the paper.
PY - 2015/7/28
Y1 - 2015/7/28
N2 - In this paper, we study reflected differential equations driven by continuous paths with finite p-variation (1≥<2) and p-rough paths (2≥p<3) on domains in Euclidean spaces whose boundaries may not be smooth. We define reflected rough differential equations and prove the existence of a solution. Also we discuss the relation between the solution to reflected stochastic differential equation and reflected rough differential equation when the driving process is a Brownian motion.
AB - In this paper, we study reflected differential equations driven by continuous paths with finite p-variation (1≥<2) and p-rough paths (2≥p<3) on domains in Euclidean spaces whose boundaries may not be smooth. We define reflected rough differential equations and prove the existence of a solution. Also we discuss the relation between the solution to reflected stochastic differential equation and reflected rough differential equation when the driving process is a Brownian motion.
KW - Reflected stochastic differential equation
KW - Rough path
KW - Skorohod equation
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U2 - 10.1016/j.spa.2015.03.008
DO - 10.1016/j.spa.2015.03.008
M3 - Article
AN - SCOPUS:84938069577
VL - 125
SP - 3570
EP - 3595
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 9
ER -