Lp Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space

This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An Lp-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.