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

TL;DR

This paper develops an $L^p$-theory for super-parabolic backward stochastic PDEs in the whole space, covering different $p$ ranges and including a comparison theorem, advancing the mathematical understanding of these equations.

Contribution

It introduces a comprehensive $L^p$-theory for semi-linear super-parabolic BSPDEs, addressing cases for $p$ in (1,2] and (2,∞), and establishes a comparison theorem.

Findings

Established $L^p$-theory for BSPDEs in different $p$ ranges.

Provided a comparison theorem for super-parabolic BSPDEs.

Extended the mathematical framework for semi-linear backward stochastic PDEs.

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.