具有一般终端时刻和非一致线性增长生成元的倒向随机微分方程的$L^p$解

$L^p$ Solutions of BSDEs with Non-Uniformly Linear Growth Generators and General Time Interval

中文关键词:  倒向随机微分方程  有限或无限终端时刻  非一致线性增长生成元  Cauchy列  $L^p~(p>1)$解

英文关键词:BSDEs  finite or infinite time interval  non-uniformly linear growth generators  Cauchy sequence  $L^p~(p>1)$ solutions

中文摘要:

      本文在生成元$g$满足对$t$不一致线性增长和终端时刻可为有限或无限时,证明了倒向随机微分方程最小$L^p~(p>1)$解的存在性. 我们的主要研究方法是构造BSDEs的一族解$\{(y^{n},z^{n})\}$, 且是$\mathbb{S}^{p}\times \mathbb{M}^{p}$空间中的Cauchy列,最后证明${(y^{n},z^{n})}$收敛到BSDEs的$L^p~(p>1)$解.

英文摘要:

      In this paper, we establish the existence of the minimal $L^p~(p>1)$ solution of backward stochastic differential equations (BSDEs) where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to $t$. The main idea is to construct a sequence of solutions $\{(Y^n,Z^n)\}$ which is a Cauchy sequence in $\mathbb{S}^{p} \times \mathbb{M}^{p}$ space, and finally we prove $\{(Y^n,Z^n)\}$ converges to the $L^p~(p>1)$ solution of BSDEs.