Comparison theorem for path dependent SDEs driven by G-Brownian motion

Abstract

Sufficient and necessary conditions are presented for the comparison theorem of path dependent G-SDEs. Different from the corresponding study in path independent G-SDEs, a probability method is applied to prove these results. Moreover, the results extend the ones in the linear expectation case.

Keywords:

• Path dependent SDEs
• order preservation
• G-Brownian motion

MATHEMATICS SUBJECT CLASSIFICATION:

• 60J75
• 47G20
• 60G52

Additional information

Funding

Supported in part by NNSFC (11801406).