L~(p) Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space

摘要

This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L ~p -theory is given for the Cauchy problem of BSPDEs, separately for the case of p ∈(1,2] and for the case of p ∈(2,∞). A comparison theorem is also addressed.