W-symmetries of backward stochastic differential equations, preservation of simple symmetries and Kozlov’s theory

Abstract

In this paper, we study the determining equations of W-symmetries for backward stochastic differential equations (BSDEs). We have proved that each simple random symmetry of multi-dimensional BSDE can be preserved under simple deterministic change of coordinates. Finally, we study the use of symmetries in studying BSDEs, and find that symmetries of BSDE can not form Lie algebra.