Applied Mathematics and Optimization, Vol.65, No.2, 175-219, 2012
L-p 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 L (p) -theory is given for the Cauchy problem of BSPDEs, separately for the case of pa(1,2] and for the case of pa(2,a). A comparison theorem is also addressed.
Keywords:Backward stochastic differential equation;Stochastic partial differential equation;Backward stochastic partial differential equation;Bessel potentials