| $L^p$ Solutions of BSDEs with Non-Uniformly Linear Growth Generators and General Time Interval |
| Received:October 18, 2014 Revised:September 02, 2015 |
| Key Words:
BSDEs finite or infinite time interval non-uniformly linear growth generators Cauchy sequence $L^p~(p>1)$ solutions
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11371362) and the Fundamental Research Funds for the Central Universities (Grant No.2012LWB48). |
| Author Name | Affiliation | | Gaojie LU | Department of Mathematics, Tongji Zhejiang College, Zhejiang 314000, P. R. China | | Long JIANG | School of Sciences, China University of Mining and Technology, Jiangsu 221116, P. R. China | | Depeng LI | School of Sciences, China University of Mining and Technology, Jiangsu 221116, P. R. China | | Shengjun FAN | School of Sciences, China University of Mining and Technology, Jiangsu 221116, P. R. China |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.01.014 |
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