$L^p$ Theory for Super-parabolic Backward Stochastic Partial Differential Equations in the Whole Space

Abstract

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 $p\in (1,2]$ and for the case of $p\in (2,\infty )$. A comparison theorem is also addressed.

References in corpus (2)

• On the Itô-Wentzell formula for distribution-valued processes and related topics
• Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations

Cited by in corpus (1)

• $W^{m,p}$-Solution ($p\ge 2$) of Linear Degenerate Backward Stochastic Partial Differential Equations in the Whole Space