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 partialdifferential equations (BSPDEs for short) of super-parabolic type. An$L^p$-theory is given for the Cauchy problem of BSPDEs, separately for the caseof $pin (1,2]$ and for the case of $pin (2, infty)$. A comparison theorem isalso addressed.